sin* (t) – cos*(t) – cos²(t) = 1 sin²(t)

Q: sin 2x Verify 1+ cos 2x = tan x.

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Q: (sin°(3x) + sin²(3x)) cos(3x) dx

A: We have to find the indefinite integral.

Q: (csc x- cot x)2 = 1- cos x %3D 1+ cos x

A: To prove: (csc⁡x−cot⁡x)2=1−cos⁡x1+cos⁡x We know that csx = 1sinx, cotx=cosxsinx

Q: sinr cos (x - y) - cosx sin (x - )

A: As we know that the trigonometric identities: sinA-B=sinAcosB-cosAsinB   Given:…

Q: sin'x+ cos x sinx 3 ,2. tan x sec x = 2 cos"x

A: use simple trigonometric relations to prove it.

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

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Q: Cotx-tanx=cos(2x)/sin(x)cos(x)

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Q: Prove the Identity

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Q: Verify the identity.

A: Use the trigonometric identities sinA+sinB=2sinA+B2cosA-B2 and cosA+cosB=2cosA+B2cosA-B2 to simplify…

Q: Prove the identity. sin'x cos'x = (cosx-cos x) sinx 3. cos x- cos x) sinx

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Q: SIn (-x) In x if x 0

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Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

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

A: Given; Sin(-x)[Sin(-x)+1].

Q: cos(-x)+sin(x=x) Q4 prove that sinx 2

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Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

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Q: 2. cotx = sin xsin π 2 --x+cos² x cotx

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Q: cos(x) – cos³ (x) = cos(x) sin²(x)

A: Here we use basic trigonometric relations,  We have,      Sin²(x) +Cos²(x) = 1         1— Cos²(x) =…

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: tan x -cot x sin x cos X %3D tan2x-cot2x 1-sin x %3D 1+ sin x 4. (sec x- tan x)² 3.

A: 3)tanx-cotxtan2x-cot2x=sinxcosxL.H.Stanx-cotxtan2x-cot2x=tanx-cotxtanx+cotxtanx-cotx=1tanx+cotx=1sin…

Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

Q: Show that

A: Given: verify that secx=sinxcosx+cosx1+sinx for verifying given identity, we solve left hand side…

Q: sin x = csc 2x cos x cos 3x sec 2x

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Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: sin4 x cos5 x dx

A: To solve: The integral ∫ sin4xcos5x dx Formula used: cos2x=1-sin2x Power rule of integration:…

Q: sin 2x+sin x dx Vsin2x -cos x v.

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Q: sin 2x cos x + cos 2x sin x = −1

A: sin(x+y)=sin(x).cos(y)+cos(x).sin(y) if sin (θ)=-1       then  θ=(2nπ+3π/2)  where n is an integer

Q: sinx 0 cosx –sinx cosx is non singular for all values of x. 1 lect one:

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Q: integral sin2 x cos3 x

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Q: cos² (In x) sin²(In x)

A: Given: I=∫cos2(lnx)sin2(lnx)xdx

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

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Q: sin(5x)+ sin(3x) tan(4x)= cos(3x)+ cos(5x)

A: We have to prove the identity

Q: sin 2x+cos2x+1 1- Prove cot x %3D sin 2x-cos 2x+1

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Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: 1+sin x+cosx 1+cos x (b) 1+sinx-cos X sin x

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Q: cos 2x-sin x 4. -(tan x +secx) %3D sin 2x - cos x

A: Given: prove that cos2x-sinxsin2x-cosx=-tanx+secx For verifying given expression, we solve left hand…

Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

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Q: secx-tanx cos x secx+tanx 1+sinx

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Q: Find exact function values for: a. sin(α/2) b. cos(α/2) c. tan (α/2) cosα = 12/13, (3π)/2 < α <…

A: The given trigonometric ratio is cosα=1213 ,where3π2&lt;α&lt;2π (a) To find the value of sinα2…

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: sin x cos x tan x = 1 – cos² x -

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Q: Lim Sin 2x Sin 2x |- CoS1ox

A: Given: L=limx→0sin2x1-cos10x+sin2x2x

Q: secx-11-cos.x sinx secx +1

A: We have to prove

Q: sin- In2| 4+ tan¬'cos- dx 2 2 1+ cos- |4+ tan-'cos= 2 2sin- In2| 4+ tan-'cos- |dx 2 2 A 1+ cos2…

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Q: التاريخ Sinho SechG)

A: Answer and explanation is given below...