sec" (*) 1 - tan?(x) cos? (x) %3D sin(x) + sin(x) sin“ (æ) – cos“ (x) = -

Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

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

A:

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

A:

Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

A:

Q: COs x 10. S V4-sin2 x

A:

Q: lim x→0 (sin10(x)cos(8x))/x=?

A:

Q: Evaluate the integral.

A:

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

A:

Q: sin x cos 4x 32) lim X0 X+X cos 5x

A: Consider the given limit

Q: cos x - sec x = 0

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

Q: =) S sin6 x+cos6 x sin³ x cos³ x dx

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: sin (2.x) cos (3x) dx

A: Integration:

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

A:

Q: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

Q: 75. sin x cos x dx 76. sin 2x sin (cos 2x) dx

A: as per the company guidelines, I can solve only one question.

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 1+sin x/cos x + cos x/1 + sin x = 2 sec x

A: Given:1+sinxcosx+cosx1+sinx=2secx

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: 2. 2. COS X Sinx lim 4x-X

A:

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

A:

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

A:

Q: Find integral.

A: To find the integral  I = ∫sin10x cos x dx

Q: 1. cos x 1 - sin x = sec x + tan x

A:

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

A: Introduction :

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

A:

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

A:

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

A:

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

A:

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

A:

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+ sin x cs x = 2 sec x %3D Cos x 1 + sin x

A:

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: ∫ sin3 (x / 2) cos (x / 4) dx

A:

Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

A:

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

A:

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

A:

Q: 3e" - 2 sec x tan x + cos x - 3 dx 1+x?

A: Given:

Q: Scos“ x- sin' xdx x•sin³ xdx 3

A:

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

A:

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

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

A:

Q: a) / sin°(x) cos(x) dx = » / sin(x)(cos(x))² dx =

A:

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

A: Given: ∫1+sinx3cosxdx

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x