∫ ( cos 2 x- cos 2 θ/ cos x- cos θ) d x is equal to

Question

∫ ( cos 2 x- cos 2 θ/ cos x- cos θ) d x is equal to (A) 2( sin x+x cos θ)+C (B) 2( sin x-x cos θ)+C (C) 2( sin x+2 x cos θ)+C (D) 2( sin x-2 x cos θ)+C

Tardigrade Admin · Accepted Answer

∫ ( cos 2 x- cos 2 θ/ cos x- cos θ) d θ =∫ (2 cos 2 x-1-(2 cos 2 θ-1)/ cos x- cos θ) d θ =2 ∫ ( cos 2 x- cos 2 θ/ cos x- cos θ) d θ =2 ∫( cos x+ cos θ) d θ =2 sin x+2 x cos θ+C

Q. $\int \frac{c o s 2 x - c o s 2 θ}{c o s x - c o s θ} d x$ is equal to

$2 (sin x + x cos θ) + C$

$2 (sin x - x cos θ) + C$

$2 (sin x + 2 x cos θ) + C$

$2 (sin x - 2 x cos θ) + C$

$\int \frac{c o s 2 x - c o s 2 θ}{c o s x - c o s θ} d θ$
$= \int \frac{2 c o s ^{2} x - 1 - ( 2 c o s ^{2} θ - 1 )}{c o s x - c o s θ} d θ$
$= 2 \int \frac{c o s ^{2} x - c o s ^{2} θ}{c o s x - c o s θ} d θ$
$= 2 \int (cos x + cos θ) d θ$
$= 2 sin x + 2 x cos θ + C$

Q. ∫cosx−cosθcos2x−cos2θ​dx is equal to

2(sinx+xcosθ)+C

2(sinx−xcosθ)+C

2(sinx+2xcosθ)+C

2(sinx−2xcosθ)+C