Cos(x) 一+Sin (x) sec (x} I +sin (x) Cos(x)

Q: cos° x tan cos' 3 x dx

A: Indefinite integral: - The term "indefinite integral" refers to an integral that has no upper or…

Q: 7x cos х -7x - lim [sin(-2x)sin(5x)sin(7x)] 2x3cos(x) lim 5x2 х>0

A:

Q: 4 cos 4 cos dx () х3 sin3 4 - у4 - х dx

A: (1) using integration by substitution∫4 cos1x2x3 sin31x2 dxlet   sin1x2=udifferentiate both…

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

A:

Q: lim x→0 (sin10(x)cos(8x))/x=?

A:

Q: cos 2x – cos x lim sin?

A: To evaluate: limx→0cos2x-cosxsin2x Solution: We know, cos2x=2cos2x-1  ..(1)sin2x=1-cos2x      ..(2)…

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

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: Cos 2x cos X-sin 2x sin x=radical 3/2. Use 0

A:

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

A: Integration:

Q: sin-1 х — у- dx + (tan-1(yx-1))xdy = 0 | cos

A:

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

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: lim cos2x-1/sinx x-> 0

A:

Q: sin 2x 29. sin x cos 2r = sec x cos X

A: As you mentioned solve question no.29

Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

A:

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

A:

Q: cos(x) – cos³ (x) = cos(x) sin²(x)

A: Here we use basic trigonometric relations,  We have,      Sin²(x) +Cos²(x) = 1         1— Cos²(x) =…

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: 1- cos () 1- cos(x) 1- sin°(;) 1+ cos(x)

A:

Q: cOs x dx sin² x+ 2 sin x+5

A:

Q: sin x = csc 2x cos x cos 3x sec 2x

A:

Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: x2 sin x+2x cos x f'(x) = cos²x

A:

Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: cos x sin x = csc 2x cos 3x sec 2x

A:

Q: cos(2x)– cosx sin x 4. lim, »o

A:

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

A:

Q: 1+ cos(x) sin(x) 1+ cos(x) = 2 csc(x) sin(x)

A:

Q: sin4 x cos5 x dx

A: To solve: The integral ∫ sin4xcos5x dx Formula used: cos2x=1-sin2x Power rule of integration:…

Q: F CSC'x + - cos2x -cos^x -sec'x

A:

Q: sin 0- cos 0 = V2

A:

Q: sin x (1- cosx) dx (1– cos² x)

A: To evaluate the integral: ∫sinx1-cosx1-cos2xdx Solution: Evaluating the given integral:…

Q: sin 4x cos 3x sin 2x tan 3z dx

A: (NOTE- Since it seems to be a typo mistake so, assuming that in the given integral all the variables…

Q: cos x-sinxtanx=

A:

Q: ∫ sin3 (x / 2) cos (x / 4) dx

A:

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

A:

Q: sin(5x)+ sin(3x) tan(4x)= cos(3x)+ cos(5x)

A: We have to prove the identity

Q: cos(x + =) – cos(x – ) = 1 6. cos ( x 6. 6.

A:

Q: cos 2x-sin x 4. -(tan x +secx) %3D sin 2x - cos x

A: Given: prove that cos2x-sinxsin2x-cosx=-tanx+secx For verifying given expression, we solve left hand…

Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x 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: Lim Sin 2x Sin 2x |- CoS1ox

A: Given: L=limx→0sin2x1-cos10x+sin2x2x

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

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.