`(sin x + sin 3x )/( cos x + cos 3x )= tan 2x `

(sin 5x + sin 3x )/( cos 5x + cos 3x ) = tan 4x

Prove that = (sin 5x - 2 sin 3 x + sin x)/( cos 5x - cos x) = tan x

sin 2x + cos x =0

(sin x - sin y)/( cos x + cos y) = tan ""(x-y)/(2)

cos 3x + cos x -2 cos x =0

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) If alpha is a root of (i) and beta is a root of (ii), then tan alpha + tan beta can be equal to

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) If tan alpha , tan beta satisfy (i) and cos gamma , cos delta satisfy (ii) , then tan alpha * tan beta + cos gamma + cos delta can be equal to

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) The number of solutions common to (i) and (ii) is

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos ^2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin alpha + sin beta + sin gamma can be equal to