" 12.If tan "theta=sec2 alpha," prove that "sin2 theta=(1-tan^(4)alpha)/(1+tan^(4)alpha)

If tan 2 theta=sec2 alpha, prove that sin2 theta=(1-tan^(4)alpha)/(1+tan^(4)alpha)

If tan 2theta= sec 2 alpha , prove that sin 2theta=(1-tan^4 alpha)/(1+tan^4 alpha)

If tan theta = sec 2 alpha, "show that", sin 2 theta = (1-tan^(4) alpha)/(1+ tan^(4) alpha).

If sin (theta + alpha ) = cos ( theta + alpha), prove that tan theta =(1- tan alpha )/(1 + tan alpha )

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If sin theta=k sin(theta+2 alpha) prove that tan(theta+alpha)=(1+k)/(1-k)tan alpha

If sin theta=n sin(theta+2 alpha), prove that tan(theta+alpha)=(1+n)/(1-n)tan alpha

If sin theta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/(1-n)tanalpha .

If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (tan^(2) alpha sin 2 phi)/(1+ tan^(2) alpha cos 2 phi)

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))