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Find the exact value

Find the exact value-example-1

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Answer:

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)}}

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