If `sintheta+costheta=p and sectheta+cosectheta=q`, then prove that `q(p^(2)-1)=2p`

If sintheta+costheta=p and sectheta+costheta=q , then prove that q(p^(2)-1)=2p

If sintheta+costheta=pandsectheta+cosectheta=q,"then prove that "q(p^(2)-1)=2p.

If sintheta,costheta and tantheta are in G.P., then prove that cot^(6)theta-cot^(2)theta=1

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

(cosectheta)/(costheta)-(costheta)/(sintheta)=?

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

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

Let P = [theta : sintheta – costheta = sqrt2 costheta) andQ= {theta : sintheta + costheta = sqrt2 sintheta} be two sets. Then:

Prove that following identities (sintheta+sectheta)^(2)+(costheta+cosectheta)^(2)=1+(sectheta+cosectheta)^(2)

Prove that following identities (sintheta+sectheta)^(2)+(costheta+cosectheta)^(2)=1+(sectheta+cosectheta)^(2)