Question

Arrange the steps in order to solve this expression sin (3pi/4) cos (pi/12)

Answer 1

Answer: The value of the expression is $\frac{1+\sqrt{3}} {4}$.

Explanation:

The given expression is,

$\sin (\frac{3\pi}{4})\cos ( \frac{\pi}{12} )$

Step 1: Break the angles.

$\sin (\pi-\frac{\pi}{4})\cos (\frac{\pi}{4}-\frac{\pi}{3} )$

Step 2: Use quadrant concept to find the value of $\sin (\pi-\frac{\pi}{4})$

$\sin (\frac{\pi}{4})\cos (\frac{\pi}{4}-\frac{\pi}{3} )$

Step 3:Use $\cos (A-B)=\cos A\cos B+\sin A\sin B$

$\sin (\frac{\pi}{4})[\cos (\frac{\pi}{4})\cos (\frac{\pi}{3})+\sin (\frac{\pi}{4})\sin (\frac{\pi}{3})]$

Step 4: Put these values by using trigonometric table.

$(\frac{1}{\sqrt 2})[(\frac{1}{\sqrt 2})(\frac{1}{2})+(\frac{1}{\sqrt 2})(\frac{\sqrt3}{2})]$

$(\frac{1}{\sqrt 2})[(\frac{1}{2\sqrt 2})+(\frac{\sqrt3}{2\sqrt 2})]$

$(\frac{1}{\sqrt 2})(\frac{1+\sqrt3}{2\sqrt 2})$

$\frac{1+\sqrt3}{4}$

Therefore, the value of the expression is $\frac{1+\sqrt{3}} {4}$.