3. Verify the product-to-sum identities below using the sine sum and difference identities. sin x• cos y = (sin (x + y) + sin (x-y)] (1) cos x- sin y=[sin (x+ y) - sin (x-y)l (2) Begin with the right side of identity (1). Rewrite this expression using the sine sum and difference identities. (List the terms in the same order as they appear in the original list.) Simplify the above expression completely. Now verify identity (2). Rewrite the expression on the right side of this identity using the sine sum and difference identities. 1 (List the terms in the same order as they appear in the original list.) Simplify the above expression completely.

Q: How did the solution of this problem remove the fraction to turn it into just CSCx on its own as…

A: We have to use the reciprocal identity That means

Q: Suppose = cos 4- Evaluate: |dx A - 3sin sin x-4+ C © -)+c -x- 3 3sin

A:

Q: What does the following identity tell us about the derivatives of sin -1x and cos- 1 x?…

A: Explanation: Suppose that,  A=sin-1xB=cos-1x   Now we can say that,  sinA=xsinB=x  So,  x=sinA=sinB…

Q: 2. If tan x = Find the sin x and cos x in the interval xe [n. : XE T,

A:

Q: Given that the sin x = 2/5 and cos x = -1/4 with sin x in Q1 and cos x in Q3, find sin( sin x - cos…

A:

Q: 1. Explain the steps in verifying that the following equation is an identity. cos x sec x + tan x =…

A:

Q: To begin evaluating S sin*(x) · cos³(x)dx, express a. sin*x to (sin²x)²and use the identity sin²x…

A:

Q: 6. Prove the following sin (x + n) = -sin x cos x+ 2 - sin x

A: Part a,Given,           sinx+π=-sinx

Q: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

Q: Find sin(2x), cos(2x), and tan(2x) from the given informa 15 tan(x) x in Quadrant II 8 240 sin(2x) =…

A:

Q: 2. Prove the following identities. Show each step and use correct mathematical notation. a, sin (x-)…

A: Use the identity  sin(x+y)= sinx siny + cosx cosy sin(x-y)= sinx siny - cosx cosy

Q: 口 | 1. What is the frequency of the periodic function 5 sin() f(x) = %3D 3.

A: Given Data: Equation: fx=5sin3θ49 ......1 The general equation of the sinusoidal function.…

Q: snip

A: Our Aim is to establish the identity given below:-1-sinθcos (θ)=cos (θ)1+sinθ-(i)

Q: 1 Use identities to verify that 1 simplifies to one of the following functions. 1+ sin x 1- sin x…

A:

Q: Prove that the following identity is true. 1- cos t sin t sin t 1 + cos t We begin on the left side…

A:

Q: An equivalent expression to sin(-x) is: Oa) - sin(-x) b) sin(x) Oc) - sin(x) d) cos(x)

A:

Q: photo attached

A: The given identity is

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: 3 3. Find the value of cos(2x) given that sin x = -and x is in QII.

A:

Q: 8. Evaluate sin (x) cos(r)dr using an appropriate substitution.

A: here  we use the formula  ∫(xn)dx=xn+1n+1+C     according to our guidelines we can answer only…

Q: 6. When defining the inverse sine function, the domain of y = sin x is restricted to -÷<xs. a. Why…

A:

Q: Prove that the following identity is true. 1- cos t sin t 1+ cos t 3D sin t We begin on the left…

A: Simply the given trigonometric function using identities

Q: Prove that the following identity is true. sin t 1+ cos t -1- cos t sin t We begin on the left side…

A: Find your answer below

Q: Use the product-to-sum identities to rewrite the following expression. sin 16° sin 8° ..... Choose…

A: According to question given:sin(16°) sin8°We have to solve the given expression.

Q: 2. Find a reduction formula for sin" x dx. By using this formula evaluate sin® x dx.

A: The objective of the question is determine the integral.

Q: Expand sin(50) in powers of sin(0) and cos(0).

A: In this question we have to expand sin5θ in powers of sinθ and cosθ. we know,…

Q: 7. Prove the following identities. sin x 1 + cosx 1- cos x a. 1-cos x b. 1 + cos x tan? %3D sin x II

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Q: Evaluate sin(x) · In ( cos(x)) dx using substitution.

A:

Q: Let x= 2 tan theta, 0 less than or equal to theta < pi/2  simplify the expression  1/x^2…

A:

Q: 2. Suppose tan x = 3 -- with < x < 2n. Find the exact value of cos ). Show you work carefully. ensem…

A: Given problem:- tan(x) =-4/3 with 3π/2 &lt;x&lt; π To find:- Exact value of cosx2)

Q: Find an equivalent expression to sin (z+) a) sin(2)-√3 cos(z) 2 b) √3 cos(z)+sin(z) 2 O c) -…

A:

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

Q: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

A:

Q: 278. Suppose that sin(ln x) = 3, and that sin(ln y) = }. If 0 < ln x < and 0 < ln y < , use the…

A:

Q: Suppose y=sin x, what is x-value between 2pi and 4 pi corresponding to y-value of -1

A:

Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

A:

Q: 4. Use Walli's formula to evaluate 2 sin*x cos°xdx.

A: Given integral is as below:-                  ∫0π2 sin4xcos9xdx

Q: 15. Evaluate | sin° x cos xdx 3

A:

Q: Sin

A:

Q: Evaluate: [e* 1+ sin 2x dx 1+ cos 2x

A: Topic:- Integration

Q: Verify the following identities: a. sin 3x = 3 sin x-4 sin x b. 1+ cos 10x = 2 cos 5x %3D

A:

Q: 20 Establish the identity: 1- cos e sin e sin e 1 + cos e LHS Sunt

A: Let us prove the given identity.

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 3 sin(2x) =D…

A:

Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

A:

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.