" 1.(i) "sin2x

Find the general solution of each of the equations : (i) sin2x=-(1)/(2) (ii) tan3x=-1

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

Consider the equation 5sin2x+3sinxcosx-3cos2x=2.......... (i) sin2x-cos2x=2-sin2x........... (ii) The number of solutions common to equations (1) and (2) is (A) 0 (B) 1 (C) finite (D) infinite

Differentiate the following w.r.t. x: (i) sin^(-1)2x (ii) tan^(-1)sqrtx (iii) cos^(-1)(cotx)

Find the principal solutions of each of the following equations : (i) sinx=(-1)/(2) "sin "(3x)/(2)=0 (iii) sin(x+(pi)/(5))=0 (iv) cos2x=0 (v) "cos"(5x)/(2)=0 (vi) cos(x+(pi)/(10))=0

Find real x such that (3+2i sin x)/(1-2i sin x) is purely real.

Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2tanx)/(1+tan^2x))\ dx

Integrate the following with respect to 'x' : (i) 1/(sin^2x) (ii) (tanx)/(cosx) (iii) (cosx)/(sin^2x) (iv) 1/(cos^2x)

(i) int 1/(4sin^2x+5cos^2x) dx (ii) int (dx)/(cos^2 x+2 sin^2x)