1. We will work with the right side of this identity. All 4 terms on the right side of the identity (the sines and cosines) will become exactly the 4 terms on the left side if they are all divided by what? To divide all 4 terms legally, multiply the right side by which is a sneaky way of multiplying by 1. 1 - tan(z) 1+tan(z) cos (2) - sin(x) cos(x) + sin(x) 1- tan(2) 1+tan(2) ? cos(x) - sin(x) cos(x)+sin(x) = Now you have: 1- tan(z) ? cos(x) - sin(x) 1+ tan(2) cos(x) + sin(x) Distribute 2. and write as 4 fractions: 1-tan(z) 1+ tan(2) 3. Now you have: Simplify all four fractions; use a quotient 1 tan(z) 1+tan(z) + 1- tan(z) 1+ tan(2) identity where appropriate: Now you have: tan(2) ? 1+ tan(z) 1 tan(2) Proven! 1 + tan(2) cos(2)-sin(2) cos(2) + sin(2)

1. We will work with the right side of this identity. All 4 terms on the right side of the identity (the sines and cosines) will become exactly the 4 terms on the left side if they are all divided by what? To divide all 4 terms legally, multiply the right side by which is a sneaky way of multiplying by 1. 1 - tan(z) 1+tan(z) cos (2) - sin(x) cos(x) + sin(x) 1- tan(2) 1+tan(2) ? cos(x) - sin(x) cos(x)+sin(x) = Now you have: 1- tan(z) ? cos(x) - sin(x) 1+ tan(2) cos(x) + sin(x) Distribute 2. and write as 4 fractions: 1-tan(z) 1+ tan(2) 3. Now you have: Simplify all four fractions; use a quotient 1 tan(z) 1+tan(z) + 1- tan(z) 1+ tan(2) identity where appropriate: Now you have: tan(2) ? 1+ tan(z) 1 tan(2) Proven! 1 + tan(2) cos(2)-sin(2) cos(2) + sin(2)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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