prove that `sinthetadotsec3theta+sin3theta,sec3^2theta+sin3^2thetadotsec3^3theta+ u p ton` terms `=1/2[tan3^ntheta-tantheta]`

prove that sin theta*sec3 theta+sin3 theta,sec3^(2)theta+sin3^(2)theta*sec3^(3)theta+... upto n terms =(1)/(2)[tan3^(n)theta-tan theta]

Prove that: sectheta sec 2theta+sec2thetasec3theta+sec3theta.sec4theta+…to n terms = 1/(sintheta) [tan(n+1)theta-tantheta]

Prove that : sin theta/cos(3theta) +sin (3theta)/cos (9theta) + sin(9theta)/cos( 27theta )= 1/2(tan27 theta -tan theta)

Prove that: (sintheta+sin3theta+sin5theta+… to n terms)/(costheta+cos3theta+cos5theta+…to n terms)= tan ntheta

Prove that :(sin5 theta+sin3 theta)/(cos5 theta+cos3 theta)=tan4 theta

Prove that :(sin theta)/(cos(3 theta))+(sin3 theta)/(cos9 theta)+(sin9 theta)/(cos27 theta)=(1)/(2)(tan27 theta-tan theta)

If tan theta+sec theta=3/2 then sin theta=

Prove that :(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

(sin3 theta+cos3 theta)/(cos theta-sin theta)=1+2xx sin2 theta

Prove that : (cos4 theta+cos3 theta+cos2 theta)/(sin4 theta+sin3 theta+sin2 theta)=cot3 theta