Question

If A = 45°, verify that cos 2A = 2 cos² A – 1.

Answer 1

Given: A = 45°; verify cos 2A = 2 cos² A – 1.

Step-wise calculation:

1. Left side: cos 2A = cos (2 × 45°) 

= cos 90°

= 0

2. Right side: 2 cos² A – 1 

= 2[cos 45°]² – 1 

= `2[(sqrt(2)/2)^2] - 1`

= `2(1/2) - 1`

= 1 – 1

= 0

Left side = Right side = 0, so cos 2A = 2 cos² A – 1 is verified for A = 45°.