Prove that `cot alpha - tan alpha =2 cot 2 alpha.`

Statement I tan alpha+2tan 2 alpha+4 tan 4 alpha + 8 tan 8 alpha+16 cot 16 alpha=cot alpha Statement II cot alpha- tan alpha=2 cot 2 alpha

Prove that tan alpha+2 tan 2 alpha+2^(2)tan^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(@)cot2^(@)alpha=cotalpha

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

tan alpha + 2 tan 2alpha + 4 tan 4 alpha + 8 cot 8 alpha =

Prove: (2)/( cot alpha tan 2 alpha ) = 1 - tan ^(2) alpha.

If 4nalpha =pi then cot alpha cot 2 alpha cot 3alpha ...cot (2n-1)alpha n in Z is equal to

If u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha), then tan(pi/4-u/2) is equal to (a) sqrt(tan alpha) (b) sqrt(cos alpha) (c) tan alpha (d) cot alpha

If u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha), then tan(pi/4-u/2) is equal to (a) sqrt(tan alpha) (b) sqrt(cos alpha) (c) tan alpha (d) cot alpha

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

Prove that (cos^2 alpha - cos^2 beta)/(cos^2 alpha*cos^2 beta) = tan^2 beta - tan^2 alpha