sin(0) d0. cos²(0) Evaluate

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A: We have to differentiate

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

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A: This question is of double angled identity.

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

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A: We need to evaluate the following integral I = ∫tantan3xcos23xdx…

Q: Verify the identity:

A: Our Aim is to verify the identity given below:-sin 3π2-x=-cos (x)  -(i)

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A: Integral.

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A:

Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

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A: Solving the problem by doing the substitution.

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A:

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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

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Q: sin e 1 cos 0 Multiply - by 1 + cos 0 1 - cos 0

A: According to the difference of squares formula, (a+b)(a-b)=a2-b2. Using the difference of squares…

Q: a/3 Find the value of cos(3x) dx.

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Q: sin2xdx 1) S7 o sin+x+cos4x

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A: To integrate: ∫sinx dxcos2x Solution: Let t=cosx Differentiating both sides, we get…

Q: / sin 3r cos 3xdx

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Q: sin 2x (1 - 2 cos 2x)? dx 6.

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Q: [*(sin³r)√1 + cos ar dr x

A: We know that integration power rule is given as  Integration of xn is xn+1/n+1.   Here i attached…

Q: [sin x √9+ cos² rdr

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Q: cos e+1 csc e 3. 3. sin 0 1- cose

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Q: sin- x - y· dx + (tan-(yx-1))xdy = 0 cos-12

A: The given differential equation is x-ysin-1yxcos -1yxdx+(tan-1(yx-1))xdy=0. Simplify to obtain the…

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Q: [cos 0 -sin 01, Verify A. AT = I ii. Let A= sin 0

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Q: sinx-1 10. Find cos x if --1. cosx a. -1 b. 2 с. 1 d. 0

A: Given: sin2 x-1cos x=-1

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Q: cos*x _8. If S(cos³x · B) dx = A. -sin x + C, what is the B? С. cos x D. secx B. csc x

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Q: sin x dx + x cos² x 5.

A: Integral of a function is the anti derivative of the function, meaning area of the graph of the…

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Q: cos*x _8. If S(cos x B) dx = - +C, what is the B? A. - sin x C. COs X В. D. cscx secx Which

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Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

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Q: CoS X Which of these is an efficient first step in proving the identity 1+ sin x 1- sin x :? cos X

A: To prove cos x1+sin x=1-sin xcos x

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

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A: Using trigonometric formula, given trigonometric function is simplified.

Q: Find the limit.

A: We have to find the limit: limθ→0cos θ-1sin θ This is 00 indeterminate form so we can apply L'…

Q: (sin x)(cos x + 1) = 0 if 0 < x < 2n. А. п/3, 2п/3 В. О, п

A: This question is taken from trigonometry in which we have to find the roots of the given…