cos(x + y) cos(x – y) = cos² x – sin² y

Q: (cos(4x))^2=___+____cos=(___x)

A: By double angle formula , we have By taking A=4x, we get

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

A:

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

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Q: · y = sin(cos 3x) – sin x cos 3x

A: Given : Y = sin(cos3x) - sinx.cos3x Let's differentiate:

Q: | sin* x cos xdx 4 X COS X

A: This question is related to integration.solve as below

Q: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: cos x-2 cos 3x + cos 5x b. cos x +2 cos 3x + cos 5x :-tan x. %3D

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Q: COs x 10. S V4-sin2 x

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Q: sin(4-y)sin(3-y)dy

A: Use the formula sin(A) sin(B)=12(cos(A-B)-cos(A+B))Consider…

Q: (sin 0)y" - (cos 0)y' 2 %3D

A: In the given question 5, The order of the differential equation is = 3 And the equation is linear.

Q: cos.2x 25. cos.x - sinx A sinx 3-.cos x + sinx C 2:cosx + sinx A - cos.x :D D cosx -2-sinx

A:

Q: sin(3x) cos(6x) – cos(3x) sin(6x) = -0.6 X =

A: There is trigonometric identity sinA-B= sinAcosB-cosAsinB

Q: cos^2ydx+(1+e^-x)sinydy=0

A: The given differential equation is cos2ydx+1+e-xsinydy=0.

Q: b) (cosx+ Sinx)² - Cos x+sinx)(cosx-Sinac) tan 2x 2. c) 1-Cos-x - Sin2oc) Sin X - 2cos x

A:

Q: cos x - sec x = 0

A: Given equation can be written as Since secx=1/cosx Therefore, we have

Q: cos (2x) -dx C Cos (x (x)

A: Use substitution method.  Convert cos(2x) = 2cos^2(x) -1

Q: CoS 2X sin x,co

A:

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

A:

Q: Cos (x-y) t cos (Xty). COS 2cos x COSY

A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: cos x 1+ sin x = 2secx 1+ sin x cos x

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Q: cos x + sin² x + 1 dx cos² x (sin² x + 1)

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Q: cos(x + y) cosx siny = coty – tanx

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Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

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Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: cos 2x - 2 sin x- cosʻx=-3

A: Consider cos 2x-2 sin x-cos2 x=-3  . . . . . (1) We have cos 2x=2 cos2 x-1 . . . .  . . (2)

Q: cosx y = x 2 (sin -1 x) 3 y=ー cos X 6. 5.

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Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

A:

Q: Differentiate

A: Given: the function

Q: secx-1 sin x %3D V secx+1 1+cos x

A: It is basic trigonometry identity

Q: (cos(3x) sin(x) – sin(3æ) cos(x)) da

A: In the given question we need to evaluate the integral- ∫cos3xsin(x)-sin(3x)cos(x)dx , which can be…

Q: (i) * cos x + cos x tan²x dx sec?x (ii) |x – 2| dx (iii) | x²/x* + 1dx

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: BIARI dr x Cos (1-1)dt b) sin² x c) cos³ x d) - cos²x

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Q: sin 0- cos 0 = V2

A:

Q: sin x dy (2y Cosx + sin4 x) ax

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Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: sec x-1 sin x %3D secx+1 1+cos x

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Q: 3. x² sin* () dx, x² sin2 () dx, n, n, a is a constant

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Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

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Q: •π * (sin³ x)√1 + cos x dx 2

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Q: cos 2x - cos2a Integrate cos x-cosa

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Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

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

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Q: cos (x+ y) cos (x-y) cos2 x- sin2 y

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Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

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Q: cos 2x 17. cos x-sin x

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: cos (x)+cos(x+x)= 0 = cosʻ (x)+cos(T+x)=0

A: cos2(x)+cos(π+x)=0 use trigonometric identity cos(π+x)=-cos(x) The equation becomes…