Question

Find value
i) $\cos {15}^o$
ii) $\sin {75}^o$
iii) $\tan {105}^o$

Answer 1

$\cos {15}^o=\cos ({45}^o-{30}^o)=\cos {45}^o\cos {30}^o+\sin {45}^o\sin {30}^0=\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\frac{1}{2}=\frac{\sqrt{3}+1}{2\sqrt{2}}$

$\sin {75}^o=\sin ({45}^o+{30}^o)=\sin {45}^o\cos {30}^o+\cos {45}^o\sin {30}^o=\frac{\sqrt{3}+1}{2\sqrt{2}}$

$\tan {105}^o=\tan ({60}^o+{45}^o)=\frac{\tan {60}^o+\tan {45}^o}{1-\tan {60}^o\tan {45}^o}=\frac{\sqrt{3}+1}{1-\sqrt{3}}$