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

Prove the following identity: (1+tan alpha tan beta)^(2)+(tan alpha)(tan alpha-tan beta)^(2)=sec^(2)alpha sec^(2)beta

If alpha+ beta + gamma=90^(@) , then tan alpha+ tan beta + tan alpha tan beta cot gamma is __________

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 alpha=(1-cos beta)/(sin beta), then a )tan3 alpha=tan2 beta(b)tan2 alpha=tan beta(c)tan2 beta=tan alpha(d) none of these

If tan (alpha + beta) = 2 and tan (alpha - beta) = 1, then tan (2 alpha ) is equal to:

If 2tan alpha=3tan beta then tan(alpha-beta)=

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

tan^2 alpha+2tan alpha.tan2beta=tan^2 beta+2tan beta.tan2 alpha, if (A) tan^2 alpha+2tan alpha.tan2beta=0 (B) tan alpha+tan beta=0 (C) tan^2 beta+2tanbeta,tan2 alpha=1 (D) tan alpha=tan beta