Question

Find the value of $(\sin 30°+\cos 30°)-(\sin 60°+\cos 60°)$.

Answer 1

Find the value of given trigonometric expression using the trigonometry table.

Given trigonometric expression: $(\sin 30°+\cos 30°)-(\sin 60°+\cos 60°)$.

We know that, $\sin 30°=\frac{1}{2},\cos 30°=\frac{\sqrt{3}}{2},\sin 60°=\frac{\sqrt{3}}{2}$ and $\cos 60°=\frac{1}{2}$

So, by substituting these values in the given expression we get,

$$\begin{gathered} (\sin 30°+\cos 30°)-(\sin 60°+\cos 60°)=\left(\frac{1}{2}+\frac{\sqrt{3}}{2}\right)-\left(\frac{\sqrt{3}}{2}+\frac{1}{2}\right) \\ =\left(\frac{1}{2}\right)+\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{1}{2}\right)-\left(\frac{\sqrt{3}}{2}\right) \\ =0 \end{gathered}$$

Hence, the value of $(\sin 30°+\cos 30°)-(\sin 60°+\cos 60°)$ is $0$.