(sin(x) + cos(x))² = 1 + 2 sin(x) cos(x)

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

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

A:

Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: s sin² (3x) cos³ (3x) dx Hint: cos²x = 1 - sin² x 07 sin²x = 1 - cos² x

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

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Q: 7. cos 2x- cos x -2 = 0

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

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

Q: cos(x) / 16 - sin2(x) dx

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

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Q: cos 2x + 2 sin 2 x = _______

A: This question can be solved by applying the formula of cos2x cos2x=cos2x-sin2x

Q: |(sin 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

Q: 2dx 2 2 cos x√ 4tanx - tan x S-

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

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

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

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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: 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin¯' 5x)

A: some functions are given , we have to find its derivative

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: cos x sin x dx 4. sin 2x cos 2x dx

A: In some cases indefinite integrals can be converted to standard integrals using an appropriate…

Q: 11) cos x csc X tan x - 1 11) 12) cos2x - sin2x = 1 - 2 sin²x 12)

A:

Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

Q: 2x-5 4. f(x) = x2+4x-5 sin x 5. f(x) = cos x

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Q: 1-sin x dx 1-cos x 2

A: Introduction :

Q: 2 csc x 1+ cos x 1- cos x

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Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: 2 cos x+3 cos x=2 2 Cos²,

A: Given,   2 cos2x+3 cos x=2

Q: ,(xsinx+cos.x)x'cos"x - x sinx + cos.r cos³ 3 dx x°cos?x

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

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Q: f2(x) = (4x + 5)°, f3(x) = (2x² + x)/x, fa(x) = cos(3x) – 2 sin² x,

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

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: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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

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

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: Cos x dx In x (sin x) () - dæ. (In x)²

A: We have to find the value of the integral : ∫cos(x)ln(x)dx-∫sin(x)1xln(x)2dx

Q: Solve over the interval [0,2pi)

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Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: Find x where 0 ≤ x ≤ 2π. cos²x - cos x - 2 = 0

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Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

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

A:

Q: |(1+ sin x)'cos x in x) cos x cOS.

A: Given: ∫1+sinx3cosxdx