`(cos x + cos y ) ^(2) + (sin x - sin y ) ^(2) = 4 cos ^(2) ""(x + y )/( 2)`

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

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

cos ^(2) 2x -cos ^(2) 6x = sin 4x sin 8x

Solve(cos y + y cos x ) dx + sin (x - x sin y) dy = 0

y - cos y = x : (y sin y + cos y + x)y' = y

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ""(x)/(2) tan ""(y)/(2))

If cot theta = cos (x+y) "and" cot phi = cos (x-y), "show that" tan (theta- phi)=(2sin x sin y )/(cos^(2) x + cos^(2) y)

Prove that, cos 4 x - cos4 y = 8(cos x - cos y)(cos x + cos y)(cos x - sin x)(cos x + sin y)

Eliminate x and y from the following equations : a sin ^(2)+ b cos^(2) x=c, b sin ^(2) y+ a cos^(2) y=d, a tan x= b tan y .

Solve :sin x 4 cos x = sin 2x 4 cos 2x.