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

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

If sin theta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/(1-n)tanalpha .

Prove that: tan^2theta=tan^2alpha ,theta=npi+-alpha,n in Z

If msintheta=n sin(theta+2alpha), prove that tan(theta+alpha)cotalpha=(m+n)/(m-n)dot

Solve the equation : tan^2 theta = tan^2 alpha

If sin theta = n sin ( theta + 2 alpha ) , show that ( n -1) tan (theta + alpha ) + (n + 1) tan alpha = 0 .

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

If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha - theta) the prove that 2 theta = alpha - [ tan^(-1) ((n-m)/(n+m)) tan alpha]

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

If msintheta=nsin(theta+2alpha) , then prove that tan(theta+alpha)cotalpha=(m+n)/(m-n) .