Prove the following :cos60° = 2cos230° – 1 = 1 – 2 sin230°

We know that,Taking LHS = cos 60° Now, solving RHS = 2cos2 30° - 1 , we get= RHSNow taking RHS = 1- 2sin2 30°= RHSHence, proved.

Q5 of 268 Page 4

Prove the following :
cos60° = 2cos²30° – 1 = 1 – 2 sin²30°

We know that,

Taking LHS = cos 60°

Now, solving RHS = 2cos² 30° - 1 , we get

= RHS

Now taking RHS = 1- 2sin² 30°

= RHS

Hence, proved.

Prove the following :

4(sin⁴30° + cos⁴ 60°) – 3(cos² 45° – sin²90°) = 2

Prove the following :

sin90° = 2sin45°.cos45°

Prove the following :

cos90° = 1 – 2 sin²45° = 2cos²45° – 1

Prove the following :

sin30°.cos60° + cos30°.sin60° = sin90°