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

Prove that (cos2theta)/(1+sin2theta)=tan(pi//4-theta)

Prove that abs(costheta-isintheta) = 1

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove that tan((pi)/(4)+theta)-tan((pi)/(4)-theta)=2tan2theta .

Prove that (1+sintheta-cos theta)/(1+sin theta+costheta)=tantheta//2

Prove that (cos(90^(@)+theta)sec(-theta)tan(180^(@)-theta))/(sec(360^(@)-theta)sin(180^(@)+theta)cot(90^(@)-theta))=-1 .

Prove that sqrt((1+sintheta)/(1-sintheta))=sectheta+tantheta,-(pi)/(2)ltthetalt(pi)/(2) .

tan ((pi)/(4)+(theta)/(2))+tan ((pi)/(4)-(theta)/(2)) is equal to