0 ≤ x ≤ π and x lies in the IInd quadrant such that Find the values of and

Given:

We know,

sin² x + cos² x = 1

⇒ cos² x = 1 – sin² x

Since,

⇒cosx will be negative in second quadrant

So,

We know,

cos 2x = 2 cos² x – 1

Since,

So,

We know,

cos 2x = 1 – 2 sin² x

Since,

So,

We know,

On rationalising:

{∵ (a + b)(a – b) = a² – b²}