Prove that at `theta=pi/3` , `sintheta(1+costheta)` is maximum.

For what value of theta , where 0 lt theta lt pi/2 does sintheta + sintheta.costheta attain maximum value?

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

(sin3theta-cos3theta)/(sintheta+costheta)+1 =

If z = (3+isintheta)/(4-icostheta) is purely real and theta in (pi/2,pi) ,then arg(sintheta + i costheta) is -

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=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 the determinant |{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}| is independent of theta .

Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

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