(i) `sec3x=-2`
(ii) `cot4x=-1`
(iii) `"cosec "3x=(-2)/(sqrt(3))`

cot x+csc x=sqrt(3)

Find the general solutions of each of the following equations : (1) sin 4x= (sqrt(3))/(2) (2) cos2x=-(1)/(2) (3) cosec 3x =(-2)/(sqrt(3)) .

"cosec"(3 - 2x) cot (3 - 2x)

Find the principle solution of the following, (i) "sin" x=(sqrt(3))/(2) (ii) "tan"x=-(1)/(sqrt(3)) (iii) cot x=-sqrt(3) (iv)cosec x=-2

Integrate the following with respect to x. (i) sin(2x +4) " " (ii) "sec"^2 (3 + 4x) " " (iii) "cosec" (ax + b) cot (ax + b) .

Prove that : (i) tan^(-1) x + cot^(-1)( x+1) = tan^(-1) (x^(2)+x+1) (ii) cot^(-1) 3 + "cosec"^(-1) sqrt(5) = pi/4

int (sec x cosec x)/(2 cot x- sec x cosec x)dx=

Find the principal values of the following : (i) sin^(-1)(sqrt(-3/2)) (ii) cot^(-1)(-sqrt(3)) (iii) cos^(-1)(-1(1)/(2)) (iv) sec^(-1)(-(2)/sqrt(3)) (v) tan^(-1)(-1) (vi) cosec ^(-1)(-1) .