Solve `1/(sinthetacostheta)+(sinthetacostheta)/(sinthetacostheta)`

Prove the following identities: (sin^3theta+cos^3theta)/(sintheta+costheta)+sinthetacostheta=1

If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+sin^(2)thetacos^(2)theta))d theta = "cosec"^(_1)(f(theta))+C , then

Prove the following identities: (cos^2theta)/(1-tantheta)+(sin^3theta)/(sintheta-costheta)=1+sinthetacostheta

If sintheta=(12)/(13) , find the value of (sin^2theta-cos^2theta)/(2sinthetacostheta)xx1/(tan^2theta)

If costheta=5/(13) , find the value of (sin^2theta-cos^2theta)/(2sinthetacostheta)xx1/(tan^2theta)

Prove that : (cos^(2)theta)/(1-tantheta)+(sin^(3)theta)/(sintheta-costheta)=1+sinthetacostheta

Solve: tan2thetacottheta=1

Prove that : (1+costheta- sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta

Prove the following identities: (tantheta-cottheta)/(sinthetacostheta)=sec^2theta-cos e c^2theta=tan^2theta-cot^2theta

Cosider the cubic equation : x^3-(1+costheta+sintheta)x^2+(costhetasintheta+costheta+sintheta)x-sinthetacostheta=0 whose roots are x_1,x_2,x_3 . The value of (x_1)^2+(x_2)^2+(x_3)^2 equals