prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

Q: 4. Verify. COSX 1+sinx = 2secx %D а. 1+sinx COSX b. cosx(1+ tanx)² = secx + 2sinx %3D

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Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: et tane)=1-Sino +Sine (Sece

A: We will prove that both sides are equal as following.

Q: cos 2x +1 sin 2x Prove that Please show proper steps sin 2x 1- cos 2x

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Q: Prompts Ssin(3x)sin(4x)dx

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Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: Verify the identity: (cos 3x - cos 5x)/(sin 3x + sin 5x) = tan x.

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Q: find integral tan 5 x sec 7 x dx

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Q: prove tany csc3-tanX =cos x CSCX Sinx tanx tcosX-

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Q: Prove sin 2x cot x (1 - cos 2x)

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Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

Q: Integral of √1-sin2x/2

A: Integral: -The function F(x)is referred to as the anti-derivative or integral of the supplied…

Q: Prove: sin (2 cosx) = 2x1-x

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Q: aie of sin(4x)+8 cos(x)+2x2 cos(4x)+8x sin(4x)+.

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Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Show that Cosx dx 9- Sin 3D

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Q: Integrate (three) of th 1) f sin6x cos3x dx

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Q: Express 2 sinx- v2 cos x in the form of Rsin(x – a), w

A: Given expression is   2 sinx -2 cosx

Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

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: 6. Verify the identity: sin x 1 + cosx 1 + cosx sin x 2 cscx %3D

A: Topic = Trigonometry

Q: Prove (Start either from the LI 1- sin x 2. cosx COSx 1+ sin x

A: To prove : 1-sinxcosx=cosx1+sinx

Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: (sinx + cosx)^2 = 1+sin(2x

A: Consider the given expression sinx+cosx2

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

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Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

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

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Q: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: 7. Show that sin (+ x) = -cosx.

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Q: sinx secx + 1 %3D 1 cosx tanx

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Q: Find sine half range for f(x) = \cos xl for -1<x<1 COSX for 7 < x < 0. f(x) for 0<x< 7. COSX

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Q: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

A: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

Q: prove that 2. = - Cotx + C |- Cosx +Sinx

A: This question is fairly based on simple formulas of trigonometry and calculus

Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: Integrate tanx+cosx-sin2x=1

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Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

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Q: sec 1.)S Intanßtanß dß

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Q: prove the identity sin^2xcos^2x+cos^(4)x=(1-sinx)(1+sinx)

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Q: Prove sinxtanx + sinx tanx 1 cosx is an identity.

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Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

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Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: find integral tan 6 x sec  4 x dx

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Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…