Question

The value of $\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\sin {30}^{\circ }$ is equal to

• A. $\sec {90}^{\circ }$
• B. $\tan {90}^{\circ }$
• C. $\cos {60}^{\circ }$
• D. $\sin {90}^{\circ }$

Answer 1

The correct option is D $\sin {90}^{\circ }$

$\sin 60°\cos 30°+\cos 60°\sin 30°$

$\Rightarrow \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}+\frac{1}{2}\times \frac{1}{2}=\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$

Also, $\sin 90°=1$

$\therefore \sin 60°\cos 30°+\cos 60°\sin 30°=\sin 90°$

Hence, the answer is $\sin 90°.$