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).`

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

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that tan alpha = 2 tan beta.

If cos alpha+ cos beta =1/3 and sin alpha+sin beta=1/4 prove that cos[(alpha-beta)/2] =+-(5/24)

Prove that (cos^2 alpha - cos^2 beta)/(cos^2 alpha*cos^2 beta) = tan^2 beta - tan^2 alpha

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

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 alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=