`(sin x + cos x)^2 + (sin x - cos x)^2`

int (sin x * e ^ (cos x) - (sin x + cos x) e ^ (sin x + cos x)) / (e ^ (2sin x) -2e ^ (sin x) +1) dx

Evaluate the following integrals. int sin x cos x (sin 2x + cos 2x) dx

Evaluate : ( sin^3x + Cos^3x ) / ( sin^2x - cos^2x )

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

If a sin^(3)x+b cos^(3)x=sin x cos x and a sin x=b cos x then a^(2)+b^(2)=

If : sin x +cos x = sin 2 x + cos 2 x , "where" 0 lt x le (pi)/(2), "then x":=

((1) / ((sec x) ^ (2) - (cos x) ^ (2)) + (1) / ((cos ecx) ^ (2) - (sin x) ^ (2))) ( cos x) ^ (2) (sin x) ^ (2) = (1- (cos x) ^ (2) (sin x) ^ (2)) / (2+ (cos x) ^ (2) (sin x) ^ (2))

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

Ltquad x rarr0 (1-cos ^ (2) (sin x) -cos (sin ^ (2) x) + cos ^ (2) (sin x) cos (sin ^ (2) x)) / (x ^ ( 6)) =

4sin x cos x+2sin x+2cos x+1=0