a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x dx x+1 f) Find the value of cos(sin- - csc-b) 3 8 g) S [(2x)2+1]2 dx dx h) S V-x2-8x-15 i) Find the value of cos(2sin-) V9-x² j) S x2 tanx sec²x -dx k) J tan?x+tanx+1 1 1) Find the value of sec(2sin-1)- cos(tan-1 Vx2-25 m) S x3 dx n) S- (x-1)Vx2-2x-3

Q: Show that Sinx+sin3x+sin5x/cosx+cos3x+cos5x=tan3x For all x for which tan 3x is dedined. Does this…

A: given that                      sinx+sin3x+sin5xcosx+cos3x+cox5x=tan3x and we have to proof…

Q: sin x 14) Simplify: sec(x) tan x A) 1 C) sec² x 7n B) tan(x) D) sin(x)

A:

Q: sec² (8t) tan² (8t) dt 16 – tan² (8t)

A:

Q: 1.) xyax ^)/√²-1²) dx + (x² - 2xy) dy = 0

A: Given : x2-y2dx+x2-2xydy=0 To Check : Differential equation is exact or not

Q: 10 - The value of x²J₁(x) x³ J(x) dx is. x-0 a) 8 (2) b) 81₁(2) c) 8/₂ (2) d. 8], (2)

A: To express: J4x  in terms of J0x and J1x Bessel's function: Jnx=∑r=0∞-1rx2n+2r1Γn+r+1 r! Series…

Q: • T/2 (3 + 7 cos³ x) sin? x dx

A:

Q: Verify the identity: sin²x (1+ncot²x) + cos²x (1+tan²x) = sin²x(n+cot²x) + cos²x(n+tan²x)

A:

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

A:

Q: Cosx 1+sinx 11. 1+sinx 2secx Cosx

A:

Q: 2dx 2 2 cos x√ 4tanx - tan x S-

A:

Q: (ez²-1-7²) Sin³z

A:

Q: Prove that sin 0 - COS 2 2 = 1 - sin 0.

A: L.H.S. =sinθ2-cosθ22R.H.S. =1-sinθ

Q: ÷(sin9t + sin5t)

A:

Q: cos(-x)+sin(x=x) Q4 prove that sinx 2

A:

Q: 2 1 + cos2x can be simplified to: O sin²x O csc² x O cos²x O sec² x

A:

Q: Prove that sin 0 COS 0 2 2 = 1 - sin 0.

A: 1. sin2θ+cos2θ=1 2. sin2θ=2sinθcosθ

Q: prove (sin4x-sin2x) / (cos4x-cos2x)   How do I prove (sin4x-sin2x)/(cos4x-cos2x) = cotx.

A: let  A=sin4x-sin2xcos4x-cos2xformula used is…

Q: 1 Find L -1 s²+4s+8] A)늘e-2t sin 2t B)- e2t cos 2t c)e-t sin 4t D) e2t cos 4t

A: Formula Used:L{eat sin(bt)}=b(s-a)2+b2