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+√(3)} {4}`.

Step-by-step explanation:

The given expression is,

`\sin ((3\pi)/(4))\cos ( (\pi)/(12) )`

Step 1: Break the angles.

`\sin (\pi-(\pi)/(4))\cos ((\pi)/(4)-(\pi)/(3) )`

Step 2: Use quadrant concept to find the value of
`\sin (\pi-(\pi)/(4))`

`\sin ((\pi)/(4))\cos ((\pi)/(4)-(\pi)/(3) )`

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

`\sin ((\pi)/(4))[\cos ((\pi)/(4))\cos ((\pi)/(3))+\sin ((\pi)/(4))\sin ((\pi)/(3))]`

Step 4: Put these values by using trigonometric table.

`((1)/(\sqrt 2))[((1)/(\sqrt 2))((1)/(2))+((1)/(\sqrt 2))((\sqrt3)/(2))]`

`((1)/(\sqrt 2))[((1)/(2\sqrt 2))+((\sqrt3)/(2\sqrt 2))]`

`((1)/(\sqrt 2))((1+\sqrt3)/(2\sqrt 2))`

`(1+\sqrt3)/(4)`

Therefore, the value of the expression is
`\frac{1+√(3)} {4}`.