4) Find the following by using the substitution z = tan D S 5 dt sint - cost cos e de ii) sin cos 0 + sin dx 1+ sin x + cos x ii) S₁ () method

Q: b) S sin 2 x cos x dx

A:

Q: Q4// Find the value of csc(sec-1 2) + cos(tan=²(-V3)).

A: Here  given as Use some trigonometric formula as

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

A:

Q: 6. sec (sin-1 x)

A: Interconversion

Q: *T/4 sec² xdx 26. 27. sin xdx TT 28. COS xdx

A:

Q: S sin5 3 x cos' 3 xdx

A:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: S COS X sin x+sin³ x dx. (b) ſ sec²x tan x+4tan³ x dx.

A:

Q: 4 sec(8) = find cot(0) 2

A: Use trigonometric rations

Q: /2 sin 2x dx Jo 3+cos (2x)

A:

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

A:

Q: Sohe nin(x+y) + cos(x+y) Solve = sin

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Q: ] 1 1-x² dx = tan¹(x)

A:

Q: what is y' of y=sin-1(cos x)

A:

Q: Number 23

A: we have to find definite intregral of given question

Q: Differentiate the following functions. Simplify and factor your answer where possible. a) f(x) = e2x…

A:

Q: Consider the function y=sin0, where 0=u+v. Suppose that u = v. Show how the Sum and Difference…

A: We will see the ans in next step

Q: 3 cos° tdt 5. 1+sint

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: dy If y = tan-[ sec2(5x² + 1) csc-3 (cos 3x)]. Find

A:

Q: Find of: y = Tan? (sin-1(x*)) %3D

A: Find the derivative

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

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: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: etermine the form that would make f sin () cos () sin(0) de

A: We have to determine the form of the given indefinite integral

Q: (Sin ² x - y) dx - tanx dy =o

A:

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

A:

Q: 1. (cos5 2x sin5 2x) dx 2. (tan5 4x tan² 2x sec2x)dx 3. (sin 5x cos 5x)dx

A: Step 1:1. I=∫(cos5(2x)sin5(2x))dxLet v=2x. Then dv=2dx, so 21​dv=2dx.Rewrite using u1 and…

Q: 1– cos(x) y = = csc(x) – cot(x) sin(x)

A: