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

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

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

Solve: tan4theta=-cot(pi/6+theta)

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

Prove that: sqrt((1-sintheta)/(1+s intheta))+sqrt((1+sintheta)/(1-s intheta)=){2/(costheta),if0lt=theta

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

For any acute angle theta; Prove (i) 'tan theta = sintheta/costheta (ii) cot theta =cos theta/sintheta

tan(pi/8)+cot(pi/8)=