Show that `(sin x+cos x)^(2)+(sin x-cos x)^(2)=2`

If tan x=(a)/(b) then show that (a sin x-b cos x)/(a sin x+b cos x)=(a^(2)-b^(2))/(a^(2)+b^(2))

(1+sin x+cos x+sin2x+cos2x)/(tan2x)=0

int(sin x cos x)/(a^(2)sin^(2)x+b^(2)cos^(2)x)dx

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

int(sin2x-cos2x)/(sin2x*cos2x)dx=?

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

((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))

If a cos x-b sin x=c show that a sin x+b cos x=sqrt(a^(2)+b^(2)+c^(2))

Show that: sin((pi)/(2)-x)=cos x

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