Chapter 13.7, Problem 6OE

To determine

To find: The expanded form of each expression by using trigonometric addition formula.

Answer to Problem 6OE

The expanded form of given expression by using trigonometric addition formula is given below.

Explanation of Solution

Given:

The given expression is as:

  $\sin \left(\frac{\pi }{2}-\frac{\pi }{6}\right)$ .

The trigonometric additional formula for $\sin$ function is given as:

  $\sin \left(x-y\right)=\sin x\cos y-\cos x\sin y$ .

The expanded form is given as:

  $\sin \left(\frac{\pi }{2}-\frac{\pi }{6}\right)=\sin \frac{\pi }{2}\cos \frac{\pi }{6}-\cos \frac{\pi }{2}\sin \frac{\pi }{6}$ .

Therefore the expanded form of given expression by using trigonometric addition formula is given above.