Prove that
`2tan^(-1)[tan((alpha)/(2)) tan((pi)/(4)-(beta)/(2))]=tan^(-1)((sin alpha cos beta)/(cos alpha+sin beta))`

Prove that , tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos^2alpha-sin^2beta)

If tan 2alpha = cot 2beta , then sec(alpha + beta) =

If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

if tan (beta/2)=4 tan (alpha/2) ,show that tan( (beta-alpha)/2)=(3sinalpha)/(5-3cosalpha)

The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^2(1/2tan^(-1)(beta/alpha))i se q u a lto (alpha+beta)(alpha^2+beta^2) (b) (alpha+beta)(alpha^2-beta^2) (alpha+beta)(alpha^2+beta^2) (d) none of these

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =0

If (cos^(4)alpha)/(cos^(2)beta)+(sin^(4)alpha)/(sin^(2)beta)=1, then provet that (cos^(4)beta)/(cos^(2)alpha)+(sin^(4)beta)/(sin^(2)alpha)=1.