Prove that `sintheta (1 + Costheta)` is the greatest at `theta=pi/3`

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

Prove that: sqrt((1-sintheta)/(1+sintheta))= sec theta- tan theta when (-pi/2) < theta < pi/2 and -sec theta+tan theta when pi/2< theta< (3pi)/2

prove that- (sintheta+1-costheta)/(costheta-1+sintheta)=(1+sintheta)/costheta

Prove that (Sintheta)/(1+Costheta)+(1+Costheta)/(Sintheta)=2"Cosec"theta

Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"theta

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

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

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

If sintheta + 2 costheta=1 ,then prove that 2sintheta-costheta=2 .

If x=costheta(1+costheta),y=sintheta(1+costheta)," then "((dy)/(dx))" at "theta=(pi)/(2) is