1. For each expression, give a trigonometric substitution that will eliminate the radical. (a) Va? – x2 (c) Vx2 – a? (b) Va2 +x2

Q: 4. Use the power-reducing formulas to write sin?xcos²x in terms of the first powers of cosine.

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Q: What is the exact value of the COS ZXY Z? X 6. 7 8

A: Topic :- Triangle

Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: dy 2.

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Q: Find a possible formula for the trigonometric function whose values are in the following table. 6 8…

A: Let's find.

Q: Write an equivalent expression for cos4 x that does not contain powers oftrigonometric functions…

A: Given cos4 xUse the formula cos 2x=2 cos2x-1                      ⇒cos 2x+12=cos2x

Q: Use the trigonometric substitution to write the algebraic expression             √(9 − x2) ,  x = 3…

A: The algebraic expression can be converted to trigonometric functions by substituting trigonometric…

Q: Find a possible formula for the trigonometric function whose values are in the following table. 6 8…

A: First, we will plot these points on the graph.

Q: (c) Under the assumption that x = ´cos 0 2 sin 0, use an appropriate right triangle to cos³ 0…

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Q: Reduce the trigonometic expression below to an algebraic expression written in terms of x.…

A: Given:The trignomentric expression is  sin(cos-1(x2−1)).

Q: 1. Use trigonometric substitution to evaluate each of the following. (») /: dx x² + 4x + 3 (b) dx (4…

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Q: 1 dr r/1+ x6 (use trigonometric substitution) 3.

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Q: If sin (B) = -1/3 with B in QIII, find csc (B/2). %3D

A: We have to solve the problem

Q: ) P2 (1, -3) Solution:

A: Given the data:

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

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Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Question in image.

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Q: If you are going to evaluate the x²+16 using trigonometric substitution, the answer is =-csc*Ø + C,…

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Q: When a and b are real, we define elatiblx with the equation ela+ ibix = eax , eibx e"(cos bx + i sin…

A: we know that am+n=am.an similarly, ea+ibx=eax+ibx=eax.eibx now, we know that eiθ=cosθ+isinθ

Q: dx If x2 – 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: 11 Suppose that ß is an acute angle with csc B . Compute the exact value of cos B. You do not have…

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Q: tan(los +1(-)

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Q: Use an identity to solve the equation 4sin2 x + 4cos x - 5 = 0 on the interval [0, 2π).

A: To solve the equation 4sin2x+4cosx-5=0 on interval 0,2π. Solution: We know that sin2x=1-sin2x So,…

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

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Q: For each expression, give a trigonometric substitution that will eliminate the radical. (a) √ a² −x²…

A: a a2- x2Put x = asinθ=a2- asinθ2= a2 - a2sin2θ=a21-sin2θ= a2cos2θ=  a.cosθ

Q: Write the given expression as an algebraic expression. sin(arcsin x + arccos x) 2 1- x* + X 2 + 1 1-…

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Q: Make the indicated trigonometric substitution in the given algebric expression and simplify. Assume…

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Q: Complete the statement by referring to a graph of a trigonometric function.

A: Given, x→π4+ limx→π4+cosx cosπ4=12 function is continous so limit is same as x=π/4

Q: If the identity sin (x + a) = sin x cos a + cos x sin a is differentiated with respect to x, is the…

A: The equation is differentiated with respect to x. a is constant with respect to x.

Q: Find a possible formula for the trigonometric function whose values are in the following table. 0 4…

A: To find the formula for the Trigonometric function using the given table.

Q: What is the formula for cos (A/2)

A: We have to find a formula for cosA2

Q: (3x-2) dx x²+ 2x + 15

A: the given problem is solved below in detail.

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify complet…

A: Given that,                                                    4 - x2   According to the question,…

Q: 3. Evaluate the following using trigonometric substitution. Show all necessary solutions. dr (e) [*.…

A: To evaluate-  the given integral.

Q: Evaluate the following expressions. Enter exact answers using fractions. 12 sin cos 13 :)) -D -1 tan…

A: Given, sincos-1-1213 tansin-1-45 We have the evaluate the expression and write the exact values.

Q: Find |xV9x? +1 dx by using the trigonometric substitution of 3x = tan 0.

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Q: Evaluate the following using the TRIGONOMETRIC SUBSTITUTION METHOD: 1.5 dx

A: Given: I=∫dxx2x2+4 For evaluating given integral, we substitute x=2tanθ…

Q: f cosece - sin0 = m and sec0 – cos0=n,Prove that „?n) + (mn²) = 1

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Q: 3. Rewrite the following in algebraic form – NO TRIG TERMS. Sec [arctan (x/4)]

A: The given trigonometric function is: Secarctanx4  This can also be written as: Sec-1tanx4

Q: 2х— х2

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Q: Suppose 0 <m(8)<, and x=2 sec(0). What is the resulting expression if we write √x² - 4 as a…

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Q: Find a possible formula for the trigonometric function whose values are in the following table. X 0…

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Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Simplify: cos^4 A − sin^4 A

A: In this question, we need to simplify cos4 A -sin4 A.

Q: If sin (B) = -1/3 with B in QIII, find sec (B/2).

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Q: Use an appropriate identity to find the exact value of the expression. sin (165°) -N2Wa+1) 4

A: Consider the given expression: sin (165°)

Q: Find a possible formula for the trigonometric function whose values are in the following table. 3 6…

A: From the given function value table, first plot the values that are points on the graph and join…

Q: cos (20)= 2

A: