By equating the real parts of cos5θ + j sin5θ = (cosθ + j sinθ)5 Show that cos5θ = 16cos5θ - 20cos3θ + 5cosθ Also, express sin5θ as powers of sinθ.

Q: Use addition formulas and the values of sin θ and cos θ for θ = π/3 , π/4 to compute sin π /12 and…

A: To calculate sin π /12 sinπ12=sinπ3-π4=sinπ3cosπ4-cosπ3sinπ4=32·12-12·12sinπ12=3-122

Q: If sec θ = -13/6 and sin θ > 0, what is 3sinθ - cos(θ)?

A: Solving the problem by finding where the theta lies.

Q: If sinx−cosx=0, then what is the value of sin^4x+cos^4x?

A:

Q: Find all the solution to 3(1-cos theta )=1-cos^2 theta

A: Our Aim is to find the solutions to 3 1-cosθ=1-cos2θ - (i)

Q: Find all solutions in radians using exact values only.         sin 3x cos 2x + cos 3x sin 2x = 1

A: Given that: sin3xcos2x+cos3xsin2x=1

Q: ( Find all degrae solutims to Cos x- 2sinx Cosx20 Give all ansuersas exat values in radian.

A:

Q: Express as a sum or difference:6 cos 5x sin 3x

A: Known fact: sinA+B-sinA-B=2cosA sinB

Q: Express as a single sine function: 10 cos (100t - 9°) + 10 sin (100t + 19°)

A: Given the given function is 10 cos100t - 9° + 10 sin100t + 19° Apply formula cosa-b=cosa cosb + sina…

Q: Use sum or difference identities to find the general solution for the equation. Show all step cos 5x…

A:

Q: Verify the identity: (cos 4x - cos 2x)/(sin 2x - sin 4x) = tan 3x

A:

Q: What is the simplified form of cos10x - cos4x / sin10x + sin 4x

A: Using CosA-CosB and SinA+SinB formula

Q: Verify that the equation is an identity. (Hint: sin 2x = sin (x+ x)) sin 2x = 2 sin x cos x…

A: Given identity issin 2x = 2 sinx cos x prove it?

Q: Use your calculator to find sin 0 and cos 0 if the point (9.52,7.14) is on the terminal side of 0.…

A:

Q: Solve for θ 6sin^2(θ)+sin(θ)-2=

A: Explanation and solution is given  below....

Q: What is the exact value of sin4)-sec(-) -4+/2 A 2 4-/7 B -4-/7 2 4+/7 2

A:

Q: Which of the equations can be used to find the value of x A) Cos 30= x/5 B) Tan 30= 5/x C) Sin 30=…

A: Given,

Q: What vaule of 0 = sin (0/3 - 10)

A: that is equal to 0=sin(0-10) than 0=sin(-10) such that -10=sin^-1(0) that is equal to zero

Q: Verify the identity: cot2 2x + cos2 2x + sin2 2x = csc2 2x

A: The given identity is ot2 2x + cos2 2x + sin2 2x = csc2 2x

Q: 3. Evaluate without using 1 calculators: cos sin- 13 -1 Cos 5 -

A:

Q: (cos2x+sin2x)+1=2  ?

A: According to the given question, cos2x+sin2x+1=2 we have to prove L.H.S=R.H.Swe take L.H.S

Q: If  2sin2 theta  - cos2 theta = 2  then find the value of theta

A:

Q: Show that 3(sinx-cosx)*+6(sinx + cosx) +4 (sin r+cosx) = 13

A: Since multiple questions are asked, Answering first one. Repost with other question if you want to…

Q: Show that the equation has exactly one real root. 2x + cos(x) = 0 %3D

A: Our Aim is to show that the equation 2x+cos (x)=0 has exactly onereal root.

Q: Simplify - 2sin(2 – x)cos(2r + 1). O cos(x + 3) – cos(3x – 1) O sin(1 – 3x) – sin(x +3) O sin(3x –…

A:

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

A:

Q: How many solutions on the interval [0, 2020π] does the equation 1/2 sin2x + 1 = sinx + cosx have?

A:

Q: Use addition formulas and the values of sin θ and cos θ for θ = π/3 ,π/4 to compute sin 7π /12 and…

A:

Q: Show that sin³ +cos³0 sin + cos 2-sin 20 2

A: Here we use the formula of (a+b)^3 .

Q: Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°

A:

Q: sin can be expanded to: sin 4 COS 2 cos - sin sin 2 O sin 4 sin -cos - + cos –sin 2 4 2 O sin + sin…

A: Given: sinπ4+π2 To find: expand the given trigonometric expression. The formula for…

Q: Prove that sin3x/sinx - cos3x/cosx = 2

A:

Q: prove that: sin7x.cos3x-cos7x.sin3x/tan2x=cos4x+1

A:

Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: Write sin(2x) cos(7x) as a sum of trigonometric functions. sin (9x) + cos(2x) sin(7x) X

A:

Q: Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13 %3D

A:

Q: Compute without using a calculator.

A:

Q: If 16(sinx) + 16(cosx)2 10 then x-.. %3D

A: Given that 16(sin x)2+16(cos x)2=10. That is 16sin2x+16cos2x=10. We have to find x value.

Q: Cos(asin '(3%5 3/5

A:

Q: Verify the identity: tan2 2x + sin2 2x + cos2 2x = sec2 2x

A:

Q: Show that the equation has exactly one real root. 8x + cos(x) = 0 %3D

A:

Q: Show that 1 1. sec-1 x = cos-1 x = cos-1 1-x 2. cos-1x = tan-1 1+x Find the exact value 1.cos[sin-1-…

A:

Q: Find the rootof( foxs = sin (cos ces) %3D 4-

A: "Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: Write sin 5x cos 9x as a sum or difference. Express your answer with even/odd properties applied.

A:

Q: Verify the identity : 2 sin2x-1= 1- 2 cos2x

A:

Q: What is the greatest possible value for the product of 2-sinx and 3 + cos5x

A: (2-sin(x))(3 + cos(5x)) =6-3sin(x)+2cos(5x)-sin(x)cos(5x)

Q: Prove (sin10x)/(sin9x+sinx) = (cos5x)/(cos4x

A: Explanation of the prove is given below..

Q: To evaluate sin 0 do , factor sin*0 as (sin²0) ² sin® and let sin²0 = -(1- cos20). A True В False

A: To evaluate: ∫sin5θdθ Let I = ∫sin5θdθ ⇒I = ∫sin4θsinθdθ

Q: Verify the identity. 2 cos 3x sin x = 2 sin x cos x – 8 cos x sin3 x Working with the left-hand…

A: Using the product to sum identity

Q: Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's…

A: This question can be solved using the De Moivre's theorem which says eix=cosx+isinx

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.