Question

what is the value of tan 221/2
degrees​

Answer 1

-2.674621

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Answer 2

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INSHORT: TAN 22.5=$\sqrt{2}$-1

EXPLANATION:

Take θ=22.5°,2θ=45°,tan2θ=tan45°=1

Use tan2θ=2tanθ/(1-tan^2θ)=1

1-tan^2θ=2tanθ

tan^2θ+2tanθ-1=0

tanθ=(-2±√(4+4)) /2=±√2-1

But tanθ=tan22.5°>0

therefore tan22.5°=√2-1 .

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