( sin x- sin 3 x/ sin 2 x- cos 2 x) is equal to

Question

( sin x- sin 3 x/ sin 2 x- cos 2 x) is equal to (A)  sin 2 x (B)  cos 2 x (C)  tan 2 x (D) None of the above

Tardigrade Admin · Accepted Answer

( sin x- sin 3 x/ sin 2 x- cos 2 x) =( sin 3 x- sin x/ cos 2 x- sin 2 x) =(2 cos (3 x+x/2) ⋅ sin (3 x-x/2)/ cos 2 x) =(2 cos 2 x ⋅ sin x/ cos 2 x) =2 sin x

Q. $\frac{s i n x - s i n 3 x}{s i n ^{2} x - c o s ^{2} x}$ is equal to

$sin 2 x$

$cos 2 x$

$tan 2 x$

None of the above

$\frac{s i n x - s i n 3 x}{s i n ^{2} x - c o s ^{2} x} = \frac{s i n 3 x - s i n x}{c o s ^{2} x - s i n ^{2} x}$
$= \frac{2 c o s \frac{3 x + x}{2} \cdot s i n \frac{3 x - x}{2}}{c o s 2 x}$
$= \frac{2 c o s 2 x \cdot s i n x}{c o s 2 x}$
$= 2 sin x$

Q. sin2x−cos2xsinx−sin3x​ is equal to

sin2x

cos2x

tan2x