9. Prove that | sin n0/sin 0|

Q: Show that for x > 0, sin ¹x+cos -1 X = FIN 2

A:

Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

A:

Q: 2 + sin x Differentiate Y x + cos

A:

Q: d 1+ sin² (2)| dz

A:

Q: sin* x – cos* x = 1 x – cos? x

A:

Q: Differentiate Sin (m sin-1 x)

A:

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

Q: Solve for 0≤x≤ 10 3xln(sinx) + (sinx)x=4

A:

Q: 6. f tan x secx+4 cos x - dx

A:

Q: find solution set of tan-1x-cot-1x=cos-1(2-x)

A:

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: 1+tanx b) 1-tanx = tan (x + ²)

A:

Q: Find all values of x in the interval 0<_x<_2pi for which -1/2<sinx<1/2

A:

Q: Evaluate sin2xlogtanx dx

A: Given:  Let I=∫0π2 sin2xlogtan x dx To Find: To evaluate the given integral.

Q: show that sinx less than x if 0 less than x less than 2pi

A: Assume that, fx=x-sinx Differentiate f (x) w.r.t. x, f'x=1-cosx=2sin2x2

Q: Find Sor y. Sin X- xp X+1

A:

Q: Prove that fx" cos(2x)dx=sin(2x)-[x n sin(2x)-x-¹ sin(2x)dx. Do not use Table Entries. H

A:

Q: S [tan® x sec6 x + cos“ x sin“ x + sin* x] dx

A: Given that: (tan8xsec6x + cos6xsin4x+sin4x) we solve this integration by using general formulas of…

Q: 3-Expand In [x? sin³ x /vx2 +1]

A: