Answer :

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


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