Question

Find the exact value

Answer 1

Answer:

Step-by-step explanation:

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

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

substituting we get:

$tg(15)=\sqrt{{2-\sqrt{3}}\over{2+\sqrt{3}}}$