Question

If A = 45°, verify that cos 2A = 2 cos²A – 1 = 1 – 2 sin²A.

Answer 1

A= 45⁰ 

`⇒ 2A = 2xx45^0=90^0`

cos 2 A = cos `90^0 = 0`

`2 cos^2 -1 = 2 cos ^2 45 ^0-1 = 2 xx(1/sqrt(2))^2 -1=2 xx1/2 -=1-1=0`

Now, `1-2 sin^2 A =1-2 xx(1/sqrt(2)^2 )-1=1-2xx1/2=1-1=0`

∴  cos 2A = 2 cos² A – 1 = 1 – 2 sin² A