Simplify `(1-costheta)/sintheta`

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Simplify costheta[costhetasinthetasinthetacostheta]+sintheta[sintheta-costhetacosthetasintheta]

Simplify (sintheta+sectheta)^(2)+(costheta+cosectheta)^(2) .

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

Prove that : (i) (1-cosA)/(sinA)=(sinA)/(1+cosA) (ii) (costheta)/(1-sintheta)=(1+sintheta)/(costheta)

Find the value of theta , if (costheta)/(1-sintheta)+(costheta)/(1+sintheta)=4,thetale90^(@) .

Evaluate [(1+costheta)/sintheta]^2

((1+sintheta+i costheta)/(1+sintheta-i costheta))^n is equal to

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

If costheta+sintheta=sqrt(2)costheta ,then find the value of (costheta-sintheta)/(sintheta) .