Prove the following identity Sin^2xcos^5x=(sin^2x-2sin^4x+sin^6x)(cosx)

Q: Show that Sinx+sin3x+sin5x/cosx+cos3x+cos5x=tan3x For all x for which tan 3x is dedined. Does this…

A: given that                      sinx+sin3x+sin5xcosx+cos3x+cox5x=tan3x and we have to proof…

Q: Verify the identity. sin (7x) – sin (3x) = - cot (5x) cos (7x) - cos (3x) ..... Start with the…

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Q: Find SinZx, Lo52x, Tan2x Cosxニーニ 3. and X terminates in quadrant 2 Sin2x = Cos 2x = tan 2x =

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Q: prove the identity cos^3x sin^3x =(sin^3x-sin^5x)cosx

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Q: Verify the identity. sin (3x) - sin (9x) cot (6x) cos (3x) - cos (9x) Start with the numerator of…

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

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

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

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Q: Prove the identity. cos²x 1+ sinx (1– sinx)? 1- sinx

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Q: Compute without using a calculator.

A: To evaluate: sin-1sin-5π6 Solution: We know that, sin-x=-sinx and sin-1-x=-sin-1x Evaluating the…

Q: Prove the following Tanx+secx=cosx/1-sinx

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Q: Prove Cos (3x)- cos (7x)/sin (3x+sin (7x) =tan (2x)

A: To Prove: Cos3x-Cos7xSin3x+Sin7x=tan2x Formulae to be used:…

Q: Prove that sin 5x + sin 3x/4 sin x cos^3 x - 4 sin^3 x cos x = 2 cos x

A: Given: sin5x+sin3x4sinxcos3x-4sin3xcosx

Q: Show that Cosx dx 9- Sin 3D

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Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

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: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Express as a product.sin 3t - sin 7t

A: Given : sin 3t - sin 7t

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

A: Consider the given expression sinx+cosx2

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

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Q: Prove the identity. 1+ sinx cosx =2 seex cosx 1+ sinx

A: We need to prove the following identity 1+sinxcosx+cosx1+sinx = 2secx

Q: Prove the identity. cosx- cos 7x tan 3x %3D sinx+ sin 7x

A: Here we use basic formulas of trigonometric ratios to find addition and subtraction.

Q: Prove that 1-cos2x+sin2x 1+cos2x+sin2x = tan x

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Q: 51 |x* sin 3xdx 2 53 [x' sin 3xdx 55 sin 3xsin 2.xdx

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

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

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Q: Verify: 1. (sinx – cosx)² – 1 = -sin2x %3D

A: We can verify the statement as below

Q: Use Simpsons 1/3 rule to find sinx

A: Please refer to the image below

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

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

Q: Prove the below 3 sin 4x 4 cos' x sin 3x + sin' x cos 3x |

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Q: Verify the identity. sin (7x) - sin (3x) = - cot (5x) cos (7x) - cos (3x) Start with the numerator…

A: As we know that; The trigonometric identities: 1). sinA-sinB=2cosA+B2sinA-B22).…

Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

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Q: Integrate tanx+cosx-sin2x=1

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Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

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Q: sin(x - ) = -COS X 2

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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: verify the identity  1 + sec ^2 x/ 1 + tan ^2 x = 1+ cos^2x

A: Note that 1+tan^2x = sec^2x  1/sec2x= cos2x

Q: Use a sum-to-product formula to rewrite sin4z+ sin 3z as a product. sin4z + sin3z = %3D OsinD

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Q: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

A: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

Q: Prove the below 3 sin 4x 4 cos' x sin 3x + sin' x cos 3x

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

A: Explanation of the prove is given below..

Q: Integrate sin®19uelog (cosu)

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Q: Prove the identity  cotx (1-cos2x)=sin2x

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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…