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

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

Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ tan theta/2 = pm tan alpha/2 *cot 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).

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-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-tan(alpha)/(2)(tan beta)/(2))

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

If cos theta = (cos alpha - cos beta)/(1-cos alpha cos beta) , then one of the values of tan((theta)/(2)) is