If and x lies in the IIIrd quadrant, find the values of and sin 2x.

Question

Philoid · Accepted Answer

Given:

We know,

cos 2x = 2 cos² x – 1

Since,

So,

We know,

cos 2x = 1 – 2 sin² x

Since,

So,

We know,

sin² x + cos² x = 1

⇒ sin² x = 1 – cos² x

Since,

So,

Now,

sin 2x = 2(sin x)(cos x)