Question

4.

Calculate tan 112.5° using a half-angle identity.

Answer 1

`-√(2) -1`

Explanation:

`tan(\alpha/2)=(1-cos\alpha )/(sin\alpha ) \\tan(112.5)=tan(225/2)=(1-cos225 )/(sin225 )=(1+cos45)/(-sin45)=(1+(1)/(√(2) ) )/((-1)/(√(2) ) )= -√(2) -1`