Question

The value of $\sin {60}^{°}\cos {30}^{°}+\sin {30}^{°}\cos {60}^{°}$ is ______.

Answer 1

$\begin{array}{rcl}\sin {60}^{°}\cos {30}^{°}+\sin {30}^{°}\cos {60}^{°}& =& \sin ({30}^{°}+{60}^{°})[\because \mathbf{sin}\mathbf{(}\mathit{A}\mathbf{+}\mathit{B}\mathbf{)}\mathbf{=}\mathbf{sin}\mathit{A}\mathbf{}\mathbf{cos}\mathit{B}\mathbf{+}\mathbf{sin}\mathit{B}\mathbf{}\mathbf{cos}\mathit{A}\mathbf{]}\\ & =& \sin \left({90}^{°}\right)\\ & =& 1\end{array}$

Final Answer :

Hence, the value of $\sin {60}^{°}\cos {30}^{°}+\sin {30}^{°}\cos {60}^{°}$ is $\mathbf{1}$.