a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin mx cos nx. c Simplify } (cos (m + n)x + cos(m = sin mx cos nx . n)x), and hence differentiate cos mx cos nx.

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: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

A:

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

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Q: Prove that cos(sinx) = /1 – x².

A:

Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

A:

Q: s nip

A: Given z=tanα2

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 results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

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

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

A:

Q: 14. Prove that (1- cos x) csc x = 1

A:

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

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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)

A:

Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

A:

Q: prove cos^4x-sin^4x=xos2x

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: Suppose cos x = - , where n < x < * . Find the exact value of cos(x – 4) . COS

A: cos(A-B)=cos A cos B+ sin A sin B

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 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: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

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: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

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: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

A:

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

A: Topic- trigonometry

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

A:

Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

A:

Q: prove tan^4x=cos4x-4cos2x+3/cos4x+4cos2x+3

A: Basic trigonometry proof

Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

A:

Q: prove that catX+c - Cos'x+Sin2X

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Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

A:

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

A:

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

A:

Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: 4. Prove that tan x – cos x = sec x – cosʻ x - x- cos cos x – 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: . Prove only 1 of the 2 identities given. sin x 1-cosx = 2 csc x 1-cos x sinx -) 1- sin? x – sin² y…

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Q: (1+cos(x))(1-cos(x))=1/2sin(2x)tan(x)

A:

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

A: Explanation of the prove is given below..

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…