`1/(1+sin^2x)+1/(1+cos^2x)+1/(1+sec^2x)+1/(1+cosec^2x)=2`

Solve (1+sin^2x-cos^2x)/(1+sin^2x+cos^2x)

The minimum value of the function f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt(1-sin^2x)+tanx/sqrt(1-sec^2x-1)+cotx/sqrt(1-cosec^2x-1) whenever it is defined is

The minimum value of the function f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt(1-sin^2x)+tanx/sqrt(1-sec^2x-1)+cotx/sqrt(1-cosec^2x-1) whenever it is defined is

2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

sin(sec^(-1)x+"cosec"^(-1)x)

Given that cos(x/2).cos(x/4).cos(x/8)..... = sinx/x Prove that (1/2^2)sec^2(x/2) +(1/2^4)sec^2(x/4) +..... = cosec^2x - 1/(x^2)

The minimum value of the function f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt(1-sin^2x)+tanx/sqrt(sec^2x-1)+cotx/sqrt(cosec^2x-1) whenever it is defined is

If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , prove that (dy)/(dx) = 4/(1 + x^2) , 0 < x < 1

2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

int(sin^(2)x*sec^(2)x+2tanx*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx= a) (cos^(2)x)(sin^(-1)x)+C b) (sin^(2)x)(sin^(-1)x)+C c) (sec^(2)x)(cos^(-1)x)+C d) (sec^(2)x)(tan^(-1)x)+C