`(1+sinx+cosx+sin2x+cos2x)/(tan2x)=0`

sinx + cosx = (cos2x)/(1-sin2x)

cosx + sinx = cos2x + sin2x

Let Delta(x)=|(sinx, cosx, sin2x+cos2x),(0,1,1),(1,0,-1)| then Delta'(x) vanishes at least once in

(sin2x)/(1+cos2x)=tan x

Solve sin2x-cos2x=sinx-cosx

The derivative of tan^(-1) ((sinx -cosx)/(sinx +cosx)) , with respect to (x)/(2) , where x in(0,(pi)/(2)) is:

prove that [2(sin^3 x - cos^3 x )/(sinx -cosx)]-sin2x=2

(sinx+cosx)/(sinx-cos x)-(sec^(2)x+2)/(tan^(2)x-1)= , where x in (0, (pi)/(2))

(sinx+cosx)/(sinx-cos x)-(sec^(2)x+2)/(tan^(2)x-1)= , where x in (0, (pi)/(2))

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is