Question

(i) sin 60° cos 30° + sin 30° cos 60°​

Answer 1

Explanation:

$\sin60. \cos30 + \sin30 . \cos60 \\ = \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} \\ = \frac{3}{4} + \frac{1}{4} \\ = \frac{3 + 1}{4} \\ = \frac{4}{4} \\ = 1 \\ \\ \sin60 = \frac{ \sqrt{3} }{2} \\ \cos30 = \frac{ \sqrt{3} }{2} \\ \sin30 = \frac{1}{2} \\ \cos60 = \frac{1}{2}$

Answer 2

$\sin(60) \cos(30) + \sin(30) \cos(60 ) \\ lets \: see \: their \: values \\ \sin(60) = \frac{ \sqrt{3} }{2} \\ \cos(30) = \frac{ \sqrt{3} }{2} \\ \sin(30) = \frac{1}{2} \\ \cos(60) = \frac{1}{2} \\ now \: substitute \: the \: values \\ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} \\ \frac{ {( \sqrt{3}) }^{2} }{4} + \frac{1}{4} \\ \frac{3}{4} + \frac{1}{4} \\ \frac{4}{4} \\ = 1$