`(1+tan alpha tan beta)^2 + (tan alpha - 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).

Simplify be reducing to a single term : (tan alpha - tan ( alpha - beta))/(1 + tan alpha tan ( alpha - beta))

If (1)/(cos alpha * cos beta )+ tan alpha * tan beta = tan gamma , where 0 lt gamma lt (pi)/2 and alpha , beta are positive acute angles , show that (pi)/4 lt gamma lt (pi)/2

If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2 alpha + 2 tan^2 alpha tan^2 beta tan^2 gamma = 1 then sin^2 alpha + sin^2 beta + sin^2 gamma =

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

If tanalpha=(1-cosbeta)/(sinbeta),t h e n (a) tan3alpha=tan2beta (b) tan2alpha=tanbeta (c) tan2beta=tanalpha (d) none of these

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=

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 a right angle be divided into three parts alpha, beta and gamma , prove that cot alpha = (tan beta + tan gamma)/(1-tan beta tan gamma) .

If alpha+beta=theta and (tan alpha)/(tan beta) = x/y , prove that sin (alpha-beta) = (x-y)/(x+y) sin theta