sin(tan^(-alpha)),|x|<1" is equal to "

Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi/4, 3pi/4 cannot lies between (1- sin2 alpha)/(1+ sin 2alpha) and (1+ sin2 alpha)/(1- sin 2alpha) .

If sin theta=3sin(theta+2 alpha), then the value of tan(theta+alpha)+2tan alpha is

If tan beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If tan beta=(n sin alpha cos alpha)/(1-n sin^(2)alpha), show that tan(alpha-beta)=(1-n)tan alpha

If tan beta=(n sin alpha cos alpha)/(1-n sin^(2)alpha), show that tan(alpha-beta)=(1-n)tan alpha

If (sin(x+alpha))/(cos(x-alpha))=(1-m)/(1+m), prove that tan((pi)/(4)-x)tan((pi)/(4)-alpha)=m

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

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

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