Prove that the equation to the two planes inclined at an angle a to XY-plane & containing the line `y = 0, zcos beta =x sin beta` is `(x^2 + y^2) tan^2 beta + z^2- 2zx tan beta = y^2tan^2 alpha`.

If tan^(2) alpha+ 2tan alpha tan 2 beta= tan^(2) beta+ 2 tan beta tan 2 alpha, show that tan beta=+- tan alpha .

If tan (alpha- beta)= (sin 2 beta)/(5-cos 2 beta) , find tan alpha: tan beta .

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" "tan" (alpha + beta)/2=

If 2 tan beta+cot beta= tan alpha , prove that cot beta= 2 tan (alpha-beta) .

Prove that the locus of a point,tangents from where to hyperbola x^(2)-y^(2)=a^(2) inclined at an angle alpha& beta with x-axis such that tan alpha tan beta=2 is also a hyperbola.Find the eccentricity of this hyperbola.

If 2 tan beta + cot beta = tan alpha , prove that 2 tan (alpha-beta) = cot beta

If x cos alpha + y sin alpha=x cos beta+y sin beta,"show that",y=x "tan"(alpha+beta)/2

If tan ( alpha-beta) = (sin 2 beta)/(5-cos 2 beta),"find the value of " tan alpha : tan beta.

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

tan (alpha + beta) tan (alpha-beta) = (sin ^ (2) alpha-sin ^ (2) beta) / (cos ^ (2) alpha-sin ^ (2) beta)