`tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)`

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

If tan theta=(tan alpha+tan beta)/(1+tan alpha tan beta) then show that sin2 theta=(sin2 alpha+sin2 beta)/(1+sin2 alpha sin2 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).

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) then tan(alpha+2 beta)tan(2 alpha+beta)=

tan ^ (2) alpha-tan ^ (2) beta = (sin ^ (2) alpha-sin ^ (2) beta) / (cos ^ (2) alpha cos ^ (2) beta)

If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(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)