Question

Find the exact value

Answer 1

Explanation:

`sin({\alpha\over{2}})=\pm\sqrt{{1-cos(\alpha)\over{2}}}\Rightarrow sin({30\over{2}})=+\sqrt{{1-{√(3)\over{2}}\over{2}}}={\sqrt{{2-√(3)}}\over{2}}`

`cos({\alpha\over{2}})=\pm\sqrt{{1+cos(\alpha)}\over{2}}=+\sqrt{{1+{√(3)\over{2}}\over{2}}}={\sqrt{{2+√(3)}}\over{2}}`

substituting we get:

`tg(15)=\sqrt{{2-√(3)}\over{2+√(3)}}`