Solve `tan(pi/2costheta)=cot(pi/2sintheta)`

Solve tan((pi)/(2)cos theta)=cot((pi)/(2)sin theta)

If tan(pi.costheta)=cot(pi.sintheta), then: cos((pi)/(4)-theta)=..... (a) 1/2 (b) 1/sqrt2 (c) 1/(2sqrt2) (d) sqrt2/2

Let tan(2pi|sintheta|)=cot(2pi|costheta|) , where theta in R and f(x)=(|sintheta|+|costheta"|"")"^x ,xgeq1. The range of f(x) include 1 (b) 2 (c) 3 (d) 4

Prove that int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.

Prove that int_(0)^(2pi)e^(costheta)cos(sintheta)d theta=2pi .

Prove that int_(0)^(2pi)e^(costheta)cos(sintheta)d theta=2pi .

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)