If `tanx=tanycos2alpha` prove that : `tan(y-x)=[tan^2alpha.sin2y]/[1+tan^2alpha.cos2y]`

If tan 2 theta=sec2 alpha, prove that sin2 theta=(1-tan^(4)alpha)/(1+tan^(4)alpha)

If tan 2theta= sec 2 alpha , prove that sin 2theta=(1-tan^4 alpha)/(1+tan^4 alpha)

If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (tan^(2) alpha sin 2 phi)/(1+ tan^(2) alpha cos 2 phi)

If tan beta=3tan alpha, prove that tan(alpha+beta)=(2sin2 beta)/(1+cos2 beta)

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If tanbeta =(sin alpha cos alpha)/(2 + cos^(2) alpha),"prove that " 3 tan (alpha -beta).=2 tan alpha

If cos^2alpha=sin^3alpha then show that tan^6alpha-tan^2alpha=1

If tan beta = 3 tan alpha, prove that tan (alpha + beta) = (2sin 2beta)/(1+cos 2beta)

If x sin alpha = y cos alpha, prove that : x/(sec 2alpha) + y/(cosec 2 alpha) = x

If 2 tan^2 alpha tan^2 beta tan^2 gamma+ tan^2 alpha tan^2 beta+ tan^2 beta tan^2 gamma+ tan^2 gamma tan^2 alpha=1 , prove that sin^2 alpha+ sin^2 beta+ sin^2 gamma =1 .