" 9.(i) "(1)/(x)+sin x

" 9."int(sin x)/(sin x+cos x)dx

" 4.(i) "int(sin x)/(1-sin^(2)x)dx

If x-(1)/(x)=2i sin theta, show that x^(4)-(1)/(x^(4))=2i sin4 theta

" (9) "int( sin2 x)/(1+cos^(2)x)dx

Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^(-1)(sin x/(1+cos x)) (iii) sin ^(-1)((2^(x+1))/(1+4^x))

Prove that: (sin x)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=((1)/(2))(tan27x-tan x)

Show that: (sin x)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=(1)/(2)(tan27x-tan x)

If I_(1)=int_(1-x)^(x) x sin{x(1-x)}dx and I_(2)=int_(1-x)^(x) sin{x(1-x)}dx , then

"I=int(sin x)/(1+sin x)*dx

If 3x + (1)/(3x) = 3 , find : (i) 9x^(2) + (1)/(9x^2)