Question

Cos 60°xcos45° + sin 45°xsin 30°....step by step please​

Answer 1

Given:

$(\cos 60\degree \times \cos 45 \degree) + (\sin 45 \degree \times \sin 30 \degree)$

Solution:

$\therefore (\cos 60\degree \times \cos 45 \degree) + (\sin 45 \degree \times \sin 30 \degree)$

As, we know that

$\it \because \rm \cos 60\degree = \frac{1}{2} \\ \because \it \rm \cos 45\degree = \frac{1}{\sqrt{2}} \\ \because \it \rm \sin 45\degree = \frac{1}{\sqrt{2}} \\ \because \it \rm \sin 30\degree = \frac{1}{2}$

Putting the values,

$\therefore \rm (\frac{1}{2} \times \frac{1}{\sqrt{2}}) + (\frac{1}{\sqrt{2}} \times \frac{1}{2})$

$\implies \rm \frac{1}{2\sqrt{2}} + \frac{1}{2\sqrt{2}}$

$\implies \rm \bf \red{\frac{1}{4\sqrt{2}}}$