Chapter 14.3, Problem 20PPS

To determine

To Verify: Given equation is an identify or not.

Explanation of Solution

Given information:

We know that, The given expression is An equation $\cos ({60}^{\circ }\text{+θ)}=\sin ({30}^{\circ }\text{+θ)}$ .

Formula used:

Signs of trigonometric functions in different quadrants.

Calculation :

Since ${90}^{\circ }+\text{θ}$ lies 1^st quadrant, and in 1^st quadrant $\sin \text{θ}$ is positive.

  $\therefore \sin ({90}^{\circ }\text{+θ)}=\cos \text{θ}\text{.}$

Using their formula.

  $\begin{array}{l}\sin ({30}^{\circ }\text{+θ)}=\cos \{{90}^{\circ }-({30}^{\circ }-\text{θ})\}\text{.}\\ =\cos ({90}^{\circ }-{30}^{\circ }\text{+θ)}\\ \text{=cos(6}{0}^{\circ }\text{+θ)}\end{array}$