d Proof Prove that [cos x] dx - sin x. -

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

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Q: H.co/prove That;- CoS z

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Q: 2. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

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Q: 37 cot x = 0,4955; con z<x< a. sen x d. sec x) b. cos x) e. csc x c. tan x

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Q: True or false? Explain/Prove. 3. For any neN, dx+n dan [cos(-x)] = (-1)2n cos (-x).

A: Given query is to find statement is true or false.

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: (2 cos z-sin z)² dx Evaluate sin z

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Q: 3 sin° x -dx Evaluate ' cos° x

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Q: Using trigonometric substitution to solve: f cos x dx 3 (4-sin²x)2 11

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Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: g(x) = 4ecoN " sin x, (0, ] COS

A: Given data:   The given function is: g(x)=4ecosxsinx The given interval is: [a,b]=[0,π].   The…

Q: sin' xcos* x dx x cos

A: Perform integration

Q: Setting x= cos or cosho show that Tn(x)==[(x + √X²_₁ )² + (x-√x ²₁ ²]

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Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

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Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin x + 3 cos x, a = 3 %3D (F-1)'(a) = %3D

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Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

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

Q: d -(tan²(x) - dx 1 Prove that : 1+x*

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Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: sin x a) 1+cos2 x dx

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Q: sin ( 27 +1)x Prove that dx =7 for all ne N. Sin x

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Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

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Q: (.0 < x < . Using the concept of Mean Value Theorem show that cos x <

A: To show: cosx&lt;sinxx2 ; 0&lt;x&lt;π2. Proof: Let fx=cosx-sinxx2. Mean value theorem: Suppose f(x)…

Q: sin 2x dx Evaluate the definite integral: COS X

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Q: I = cos? x sin x In(cos x)

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Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: Evaluate: / [cos(x) – sin(x«) ]dr A cos(x) + sin(x) +C - cos(x) + sin(x) +C

A: In this question we will use basic of calculus i.e concept of integration. We will simply use the…

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

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Q: Lim メートo Cos aX Cos bX

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Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: cos ax dx = xe", a 2 0. (or) Evaluate x' +1 cos ax 2: Prove that x +1

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Q: sin x dx TT cos2 x + e cos x

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Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 6 sin° x+ cos° x dx sin xcos x Evaluate :

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Q: Prove 1+ sin t /cos t = cos t / 1- sin t

A: We have to prove the identity: 1+sin tcos t=cos t1-sin t Taking LHS part, LHS=1+sin tcos t×1-sin…

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

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Q: Verify the identity: [cos(x + h) - cos x]/h = cos x. (cos h - 1)/h - sin x. (sin h)/h

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: 3+(e*+3) sin x %3D tan(x³)-x

A: y=6x3+(ex+3)sinxtan(x3)-x

Q: 1 + cos X 1 - cos X

A: We are given with fraction need to evaluate.

Q: Prove the identity.  cosh x - sinh x = e -x

A: Consider the given identity of L.H.S as coshx-sinhx

Q: Ca) Prove that sin-z = -i ln(iz + (1 – z²)/²). ) Find the principal value of sin (2i) and write your…

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Q: 3) f(x) = cos (tan³(sin (x³))) %3D

A: Given, f(x)=cos5tan3sin2x5 now we apply chain rule to derivate ddxf(x)=ddxcos5tan3sin2x5

Q: Solve r-t cos x+p tan x = 0, %3D

A: The solution is given as

Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

A: