" 20."(cos x)/((2+sin x)(1+sin x)^(2))

int_(0)^(pi//2) (sin x cos x) / ((1 + 2 sin x ) ( 1+ sin x))dx =

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

((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))

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

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))

If sin x ( cos ""(x)/( 4) - 2 sin x) + ( 1 + sin "" (x)/( 4) - 2 cos x) cos x = 0 then x =

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

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

int(cos x+sin x)/(cos x-sin x)(1-sin2x)dx

(1+sin x+cos x)^(2)=2(1+sin x)(1+cos x)