Find the value of tan 22°30’.

[Hint: Let θ = 45°, use

Let, θ = 45°

As we need to find: tan 22°30’ = tan (θ/2)

∵

If somehow, we manage to get sin θ and cos θ in numerator and denominator, our problem will be solved as we know that –

sin θ = cos θ = 1/√2 (for θ = 45°)

As,

Multiplying in numerator and denominator, we get –

⇒

By applying formula of T-ratios of multiple angles-

sin 2x = 2sin x cos x

cos 2x = 2cos²x – 1 or 1 + cos 2x = 2cos²x

∴

⇒ tan 22°30’ =

By rationalizing the term, we get-

⇒ tan 22°30’ =

∴ tan 22°30’ = √2 – 1