Prove that `(1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)=2^(n+1)cos^(n)((theta)/(2))cos((ntheta)/(2))`

Prove that (sintheta +sin2theta)/(1+costheta +cos2theta)=tantheta

Prove that (1-costheta +cos2theta )/(sin2theta -sintheta)=cottheta

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

Simplify : ((cos3theta+isin3theta)^(2)(cos3theta-isin3theta)^(-3))/((cos4theta+isin4theta)^(-4)(costheta+isintheta)^(2))

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

Prove that sqrt(cot^(2)theta-cos^(2)theta)=cottheta.costheta

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

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

(sintheta+sin2theta)/(1+costheta+cos2theta)

choose the correct pair of statement : (i) (costheta+isintheta)^(n)=cosntheta+isinntheta , x is an integer (ii) (sintheta+icostheta)^(n)=sinntheta+icosthetantheta , n is an integer (iii) If z=costheta+isintheta , then z^(-1)=costheta-isintheta (iv)(z+barz)/(2)=Re(z)