Question

If sin $(C+D)=sinC.cosD+cosC.sinD$ then the value of sin ${75}^0$is

• A. $\frac{1}{2\sqrt{2}}(\sqrt{3}+1)$
• B. $\frac{1}{2}(\sqrt{3}-1)$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{2\sqrt{2}}(\sqrt{3}+1)$

$sin{75}^0$
$=sin({45}^0+{30}^0)$
$=sin{45}^{0}cos{30}^0+cos{45}^{0}sin{30}^0$
$=\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\frac{1}{2}$
$=\frac{\sqrt{3}+1}{2\sqrt{2}}$
Hence answer is A