If `tan alpha = (sin theta sin varphi)/(cos theta + cos varphi)`, prove that one of the values of `tan\ alpha/2` is `tan\ theta/2 tan\ varphi/2`.

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

If sin theta+ cos theta = sqrt(2) cos theta, (theta ne 90^(@)) then value of tan theta is

Prove that : (sin 5theta + sin 3theta)/(cos 5theta + cos 3theta) = tan 4theta

If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of tan (theta/2)=(tan (alpha/2)-tan (beta/2))/(1-tan (alpha/2) tan (beta/2)).

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of (tan) theta/2=(tan alpha/2-tan beta/2)/(1-t a n alpha/2 tan beta/2).

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

Prove that : (sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta), prove that tan theta/2=+-tan alpha/2 cot beta/2.