Question

Evaluate the following
(i) $sin{60}^{\circ }cos{30}^{\circ }+sin{30}^{\circ }cos{60}^{\circ }$
(ii) $\frac{cos{45}^{\circ }}{sec{30}^{\circ }+cosec{30}^{\circ }}$

Answer 1

(i)$sin{60}^{\circ }cos{30}^{\circ }+sin{30}^{\circ }cos{60}^{\circ }$

$\Rightarrow sin(60+30)=sin90$

=1 $\left[sin\right(a+b)=sinacosb+cosasinb]$

(ii) $\frac{cos{45}^{\circ }}{sec{30}^{\circ }+cosec{30}^{\circ }}=\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+\frac{2}{1}}=\frac{\sqrt{3}}{\sqrt{2}(2+2\sqrt{3})}$

$[cos45=\frac{1}{\sqrt{2}}sec30=\frac{2}{\sqrt{3}}cosec30=2]$