Prove that 2sin 22 1°/2 cos 22 1°/2 = 1/√2

Question

Prove that

2sin 22\(\frac{1^\circ}{2}\)cos 22\(\frac{1^\circ}{2}\) = \(\frac{1}{\sqrt{2}}\)

2sin 22 1°/2 cos 22 1°/2 = 1/√2

Answer 1

To Prove: 2sin \(22\frac{1^\circ}{2}\) cos\(22\frac{1^\circ}{2}\) = \(\frac{1}{\sqrt{2}}\)

Taking LHS,

2sin \(22\frac{1^\circ}{2}\) cos\(22\frac{1^\circ}{2}\)  ....(i)

We know that,

2sinx cosx = sin 2x

Here, x = \(22\frac{1}{2}\) = \(\frac{45}{2}\)

So, eq. (i) become

= sin \(2(\frac{45}{2})\)

= sin 45°

= RHS

∴ LHS = RHS

Hence Proved