sin (A+B) Q2 / (A) Prove the identity tanA+tanB %3D cosA.cosB dy Q2 / (B) Find for the following equation dx 1+3x y =() (3-x)

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

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

A:

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

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Q: Evaluate the integral.

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Q: 2 (tan²x + 1)√sin2x.dx= (tan², 0

A: Find your answer below

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

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 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

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

A: Integration:

Q: sin x cos" п — 1 n 2 2, | co cos"-2 x d.x Show that for cos" x dx Use this to find cos4. x dx.

A: Given, ∫cos4xdx

Q: sin 2x V2 – cos 2x dx

A:

Q: | (cos(3x) sin(x) – sin(3x) sin(x)) dæ

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

A:

Q: - y = sin² (-1) y = cos" - y = arctan 0

A: This question is based on general solution of  Trignometric function.

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: arc cos XY VI-x²

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

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: Sin 5x Cos 4x dx

A: The given integral is ∫sin5xcos4xdx.

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: sin x dx 2- cos²x CoS

A:

Q: 1+cos 4x dx 1-cos 4x Evaluate

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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: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7…

Q: cOs x dx sin² x+ 2 sin x+5

A:

Q: sinx dx cos³x (1 – sec*x)3 A)를 (1-sectx)-4 +C B)를 In(1 sec*x)3 + C c)금 (1-sec+x)-2 + C D)름…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: sin(-4x) cos 3x dx 1. 3

A:

Q: 4 cos (4x)(-4 sin (4x))dx. Evaluate the integral 4 cos (4x)(- 4 sin (4x))dx%3D

A:

Q: Find integral.

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

Q: sin 2x cos 3х dx

A:

Q: sin2x -dp- cos x+cos*x-2cos?x

A:

Q: sin x (cos x + 4) dx 1+cos²x

A: SOLUTION-

Q: BIARI dr x Cos (1-1)dt b) sin² x c) cos³ x d) - cos²x

A:

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

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

A:

Q: sin x (1- cosx) dx (1– cos² x)

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

Q: i) etan-¹x 12 1 + x² dx ii) ii) sin sin5 x dx

A: Solve the following

Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

A: We have to prove that  (Sinx+cosx)^2=sin(2x)+1

Q: sin 5x cos 3x dx

A:

Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: cos x-sinxtanx=

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

A: Given problem:-

Q: | cos(x) (8 + 4 sin²(x)) dx

A: Given Data: Integral Expression: ∫cosx8+4sin2xdx   Let, sinx=u Differentiate above equation.…

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

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Q: •π * (sin³ x)√1 + cos x dx 2

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Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

A:

Q: sec(x)cos(3x)=0 from [-pi/2, pi,2]

A: sec x cos 3x=0          [-π/2,π/2] sec x (4 cos3x - 3 cos x) = 0 [cos 3x= 4 cos3x - 3 cos x] 4 sec x…

Q: 3.Sinx sec a +2 Sinto Sinx(Secxt2)=0 sinx=D0 भा 2TT Seci=-ス 4Sin3x -sinx CoS X → Sinx(Sin?x -=Sin?x.…

A:

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