PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 5.1, Problem 38E
Solution

To find: The simplified form of the expression sinx1cosx+1cosxsinx .

The simplified form of the given expression is 2cscx .

Given information: The given expression is sinx1cosx+1cosxsinx .

Formula used: The formula of Pythagorean identity is sin2θ+cos2θ=1 and the reciprocal identity is cscθ=1sinθ .

Calculation:

Simplify the given expression using identity ab2=a22ab+b2.

  sinx1cosx+1cosxsinx=sinx2+1cosx21cosxsinx=sin2x+122cosx+cos2x1cosxsinx=sin2x+12cosx+cos2x1cosxsinx=sin2x+12cosx+cos2x1cosxsinx

Apply the formula of Pythagorean identity, sin2θ+cos2θ=1 and the reciprocal identity, cscθ=1sinθ into obtained expression.

  sin2x+12cosx+cos2x1cosxsinx=sin2x+cos2x+12cosx1cosxsinx=1+12cosx1cosxsinx=21cosx1cosxsinx=2sinx=2cscx

Therefore, the simplified form of the given expression is 2cscx .

Chapter 5 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 5.1 - Prob. 11QRCh. 5.1 - Prob. 12QRCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Prob. 64ECh. 5.1 - Prob. 65ECh. 5.1 - Prob. 66ECh. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - Prob. 69ECh. 5.1 - Prob. 70ECh. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.1 - Prob. 82ECh. 5.1 - Prob. 83ECh. 5.1 - Prob. 84ECh. 5.1 - Prob. 85ECh. 5.1 - Prob. 87ECh. 5.1 - Prob. 88ECh. 5.1 - Prob. 89ECh. 5.1 - Prob. 90ECh. 5.1 - Prob. 91ECh. 5.1 - Prob. 92ECh. 5.2 - Prob. 1QRCh. 5.2 - Prob. 2QRCh. 5.2 - Prob. 3QRCh. 5.2 - Prob. 4QRCh. 5.2 - Prob. 5QRCh. 5.2 - Prob. 6QRCh. 5.2 - Prob. 7QRCh. 5.2 - Prob. 8QRCh. 5.2 - Prob. 9QRCh. 5.2 - Prob. 10QRCh. 5.2 - Prob. 11QRCh. 5.2 - Prob. 12QRCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 73ECh. 5.2 - Prob. 74ECh. 5.2 - Prob. 75ECh. 5.2 - Prob. 76ECh. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.2 - Prob. 80ECh. 5.2 - Prob. 81ECh. 5.3 - Prob. 1QRCh. 5.3 - Prob. 2QRCh. 5.3 - Prob. 3QRCh. 5.3 - Prob. 4QRCh. 5.3 - Prob. 5QRCh. 5.3 - Prob. 6QRCh. 5.3 - Prob. 7QRCh. 5.3 - Prob. 8QRCh. 5.3 - Prob. 9QRCh. 5.3 - Prob. 10QRCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.4 - Prob. 1QRCh. 5.4 - Prob. 2QRCh. 5.4 - Prob. 3QRCh. 5.4 - Prob. 4QRCh. 5.4 - Prob. 5QRCh. 5.4 - Prob. 6QRCh. 5.4 - Prob. 7QRCh. 5.4 - Prob. 8QRCh. 5.4 - Prob. 9QRCh. 5.4 - Prob. 10QRCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.5 - Prob. 1QRCh. 5.5 - Prob. 2QRCh. 5.5 - Prob. 3QRCh. 5.5 - Prob. 4QRCh. 5.5 - Prob. 5QRCh. 5.5 - Prob. 6QRCh. 5.5 - Prob. 7QRCh. 5.5 - Prob. 8QRCh. 5.5 - Prob. 9QRCh. 5.5 - Prob. 10QRCh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Prob. 44ECh. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5.5 - Prob. 56ECh. 5.5 - Prob. 57ECh. 5.6 - Prob. 1QRCh. 5.6 - Prob. 2QRCh. 5.6 - Prob. 3QRCh. 5.6 - Prob. 4QRCh. 5.6 - Prob. 5QRCh. 5.6 - Prob. 6QRCh. 5.6 - Prob. 7QRCh. 5.6 - Prob. 8QRCh. 5.6 - Prob. 9QRCh. 5.6 - Prob. 10QRCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Prob. 33ECh. 5.6 - Prob. 34ECh. 5.6 - Prob. 35ECh. 5.6 - Prob. 36ECh. 5.6 - Prob. 37ECh. 5.6 - Prob. 38ECh. 5.6 - Prob. 39ECh. 5.6 - Prob. 40ECh. 5.6 - Prob. 41ECh. 5.6 - Prob. 42ECh. 5.6 - Prob. 43ECh. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Prob. 46ECh. 5.6 - Prob. 47ECh. 5.6 - Prob. 48ECh. 5.6 - Prob. 49ECh. 5.6 - Prob. 50ECh. 5.6 - Prob. 51ECh. 5.6 - Prob. 52ECh. 5.6 - Prob. 53ECh. 5.6 - Prob. 54ECh. 5.6 - Prob. 55ECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - 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