1. sin (-x)(sin(-x) + 1)

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: 2 cos² x√4 tan x S tan² x dx

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Q: · y = sin(cos 3x) – sin x cos 3x

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

Q: 2 cos^2 x-sin x -1=0

A: 2cos2x-sinx-1=0⇒1-sinx-2sin2x=0⇒sinx=-1, sinx=12⇒x=3π2+2πn, x=π6+2πn, x=5π6+2πn

Q: 8+tan x dx 1-sin?x i.

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Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

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Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: 1+ sin x f(x) 1- cos x

A: on differentiation with respect to x we get

Q: 9. Sin 2X dx COS 2X

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Q: 5) 3tan-1x + sin-x = 4

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Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

Q: sin (3x+1)dx 4 cos (3x+1) C

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Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

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Q: √2 2 sin-¹(x)dx

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Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: Differentiate.  y =cos x /(1 - sin x)

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Q: dr de sin - r- cos + eª cos = 0

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Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: - 3in 2 X sin X- COSX

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Q: 2 sin(x) cos(x) V3 cos(x

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Q: cos(x) + s(3x)+ 25 cos(5x)+..) 4 Ans. + sin(x)- sin(2x)+ sin(3x)– ...

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Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

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Q: Differentiate  x sin−1(x)  with respect to sin−1x.

A: Using derivative of one function w r to another function.

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

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Q: )Find the anti derivative for sin(x^2) 2x

A: we have to find the anti derivative of ∫sinx22xdx...............1 first we put in place of x2 =z…

Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

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Q: Suppose y=sin x, what is x-value between 2pi and 4 pi corresponding to y-value of -1

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Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: 3/2 6x sin' - r-sin x) Evaluate: +3x dx. x-sin x

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Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

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

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: Differentiate x sin-1 (x) with respect to sin¯'x. х.

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Q: 5. sin 2 x=cos X

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Q: (2 In sin x)3 15. S tan x

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Q: 4x 3x + cos (2x² + 1) tan? x) x (1+ sin² dx

A: Here We have to evaluate;  a) ∫4x3x+cos(2x2+1)dx b) ∫tan2x(1+sin2x)cos2xdx

Q: Problem Differentiate. y = In(sin (x²))

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Q: 2. y = tan-1(sin 3x) + cos-(cos x)

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

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…

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment