`(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 3x + sin x)/(cos 5 x - cos x)= tan x

((sin 7x + sin 5x ) +(sin 9x + sin 3x))/( (cos 7x + cos 5x ) + (cos 9x + cos 3x ))= tan 6x

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

Prove that ( sin x- sin y )/( cos x + cosy ) =tan (( x-y )/( 2))

(sin 3x + sin x ) sin x + (cos 3x - cos x) cos x =0

Function f(x) = (lambda sin x + 6 sin x)/(2 sin x + 3 cos x) is monotonic increasing if

Prove that (sin 9x+sin7+sin 3x+sin 5x)/(cos 9x+ cos 7x+ cos 3x+cos 5x)=tan 6x .

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 (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