=" प्रश्न 20."(cos2x)/((cos x+sin x)^(2))

int(cos2x)/((cos x+sin x)^(2))dx

int(cos2x)/((sin x+cos x)^(2))dx=

Integrate the functions (cos2x)/((cos x+sin x)^(2))

(cos2x)/(sin ^(2) x cos^(2) x)

(cos2x)/(cos x-sin x)=cos x+sin x

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

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