Show that the following general equation x = c1 cos(/t) + c2 sin(\/t) k m can be transformed into: C cos(/ t + ¢) x = m Write down constant C and O in terms of c, and c,! Hint: use a trigonometric identity!

Q: Verify the following identity. 1+ cos 2x cotx%D sin 2x

A: Recall: sin2x = 2 sinx cosx cos2x = 2cos2x -1 cotx = cosxsinx

Q: Prove the identity cos e cos e = tan 0. 1+sin e

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Q: Determine the values of sin 20, cos 20, and tan 20, given 3 cos 0 = 1 and 0 ≤ 0 ≤ T 2°

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Q: , Find the exact value of cos (a – B) given that cos a = - and sin 3 = -0 for a in Quadrant III and…

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Q: 2. Use the fundamental identity to write two functions for cos a in terms of sin a. Indicate which…

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Q: If sin A = 3 with A in QII, find the following. A COS

A: Pythagorean theorem: -A right-angled triangle is subject to the Pythagorean theorem formula. In a…

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

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Q: 6. Explain the steps in verifying that the following equation is an identity. sec x sin x = cot x…

A: We have given equation  Taking left side of equation  LHS = secxsinx-sinxcosx           =…

Q: Verify the identity: cos A sin' A 1 %3D 1 – cos A -

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Q: Va? – x²

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Q: 3. Use De Moivre's Theorem to find the identity of the following: a. cos 80 b. sin 90 C. cos 100 d.…

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Q: d) Verify the identity sin 0 tan 2, 1+ cos e

A: To prove:

Q: 5. Is the equation cos 0 – sin 0 =1 an identity? If so, verify it. If not, explain why. %3D

A: The trigonometric equation is an identity if it is true for all cases. To check if the equation is…

Q: Verify that the trigonometric equation is an identity. csc 0 1+ sin 0 - 1+ csc 0 cos 20 Which of the…

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Q: 1+ cos(x) sin(x) sin(x) 1- cos(x)

A: To prove:

Q: 4. Prove that the identity is true. 1- cos“ e sin? e 1+ cos e

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Q: verify the trigonometric identity below. 1+ sin(2θ)+(sin(θ)+cos(θ))^2

A: Given data 1+sin2θ=sinθ+cosθ2

Q: If sin (A)= 12/13 with A in QII, find cos (A/2). cos (A/2)=________

A: In second quadrant cos is negative

Q: (cos 0 + sin 0)² – 1 = 2 sin Ocos0 %3D

A:

Q: Find the exact value of tan α = 4/3, π < α < 3π/2, and tan β = 5/12, 0 < β < π/2 under…

A: Given condition - π<α<3π2    that means α is in 3rd quadrant.0<β<π2     that means β is…

Q: Prove the identity on a separate sheet of paper. tan 6+ sin e cos 2 tan e

A: In this question we have to prove the following identity.

Q: Find the exact value of cos(A+B) if sin A = with A in QI and sin B 5 with B in QID = -

A: Given: sinA=35sinB=-513 To find the exact value of cos(A+B) COS(A+B)=COSACOSB-SINASINB COS2θ+SIN2θ=1

Q: 5. Is the equation cos 8- sin 0 =1 an identity? If so, verify it. If not, explain why.

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Q: 5. Use a half-angle identity to find the exact value of sin cos x = 12

A: To find the value of sin

Q: Verify the following identities: sin 20 – tan 0 tan 0 cos 20

A: Solved below

Q: Prove the following identity. Include a complete solution in proper form. (sin Ø + cos Ø) = 1 + 2…

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Q: 5. Is the equation cos 0 - sin 0 = 1 an identity? If so, verify it. If not, explain why. %3D

A: As we know that an identity is satisfied by any value of variable . Let's check for given equation .

Q: cos s e + cscOsind| 2. sin²e

A: To simplify cos2θsin2θ+cscθsinθ

Q: if sin A=3/5  A in QII find cos A/2

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Q: Let sin 0 = 12/13, and cos 0 = 5/13, and find the indicated value. %3! %! sec 0 = %3D

A: Given ,  sin θ = 12/13  cos θ = 5/13 We have to find sec θ Since ,

Q: 4. Prove the following identity: 1 - tan?a cos2a %3D sec?a Sin(420) b sin7d

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Q: Verify the identity shown below. cos e sec e – sin 0 tan 0

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Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: 1. Use an identity to find the value of cos (0+ 90°). sin 0 cos 0 O - cos 0 O - sin e

A: We have to find the following

Q: 5. Is the equation cos 0 – sin 0 = 1 an identity? If so, verify it. If not, explain why.

A: We have to check

Q: If sin A = 3/ 4with A in QII, find cos A.

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Q: Find the exact value of the expressions cos(a+B), sin (a+B) and tan (a+B) under the following…

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Q: 5. Which of the following quantities is undefined? (a) sin-'(-}) csc-"(}) (b) cos-'(2) (d) csc-'(2)

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Q: (1 + sinx)? + cos²x = 2 1+ sin x

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Q: Prove identity cos ( +a) = - sin

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Q: Suppose that tan t 12 and sin t 20. %3D a. What is the exact value of sin t? b. What is the exact…

A: Given that  tan t=-125sin t <0 To find: (a) The exact value of sin t. (b) The exact value of cos…

Q: Let 0 e (7, 27) be' such that tan 0 = . Find sin 0 and cos 0.

A: From the given problem: tanθ=12tan2θ=14sec2θ-1=14sec2θ=54secθ=±521cosθ=±52cosθ=±25  When θ belongs…

Q: (9) Verify the following (a) cos e + sin 0 tan e = sec e %3D

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &…

Q: photo is attached

A:

Q: 12. Verify the following trigonometric identities. tan (x) sin (2x) = 2 – 2 cos (x)

A: To verify the identity: tan(x)sin(2x)=2-2cos2(x) Solution: We know, tan(θ)=sin(θ)cos(θ)…

Q: 1- sin(x)cos(x) sec(x) – sin(x): cos(x)

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Q: Prove the identity sin30 cos 30 = 2 cos e sin 0

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Q: What happens if you take B = A in the trigonometric identity cos (A - B) = cos A cos B + sin A sin…

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