" (ii) "cot(4x-5)cosec(4x-5)

Evaluate the following integrals. (i) 12/((4x - 5)^3) + 6/(3x + 2) + 16 e^(4x + 3) (ii) 15/(sqrt(5x - 4)) - 8 cot (4x + 2) "cosec" (4x + 2) .

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

Evaluate : int cot^(3)x cosec^(4)x dx

Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5sec x+4 cos x (iv) cosec x (v) 3 cot x+5 cosec x (vi) 5sinx-6cosx+7 (vii) 2tanx-7secx

Evaluate: (i) int cot^2x cosec^4xdx (ii) int cosec^4xdx

int (dx)/(cosec 4x-cot 4x)

"cosec"[2 cot^(-1)(5) + cos^(-1)(4/5)] is equal to

e^(-5x)cot 4x

int_(0)^(pi//4) cot x. " cosec"^(2) x dx

If sin^(-1)(x/5) + cosec^(-1) (5/4) = pi/2 , then the value of x is