Q5 of 268 Page 4

Prove the following :
sin90° = 2sin45°.cos45°

We know that,

sin (90^o) = 1

Taking LHS = sin 90° = 1

Now, taking RHS

= 1

= R.H.S.

Hence Proved

Prove the following :

cos(A – B) = cos A. cos B + sinA . sin B if A=B=60^o

Prove the following :

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

Prove the following :

cos60° = 2cos²30° – 1 = 1 – 2 sin²30°

Prove the following :

cos90° = 1 – 2 sin²45° = 2cos²45° – 1

Prove the following :sin90° = 2sin45°.cos45°