Question

What is$\sin \left(x\right)$ times $\sin \left(x\right)$?

Answer 1

Product of trigonometric ratios:

$\sin x\times \sin x={\sin }^{2}x$

By using trigonometric identity

$$\begin{gathered} \mathbf{\because }\mathbf{}{\mathbf{sin}}^{\mathbf{2}}\mathbf{}\mathbf{x}\mathbf{+}{\mathbf{cos}}^{\mathbf{2}}\mathbf{}\mathbf{x}\mathbf{=}\mathbf{1} \\ \therefore {\sin }^{2}x=1-{\cos }^{2}x \end{gathered}$$

Hence, $\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ times $\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ is ${\mathbf{sin}}^{\mathbf{2}}\mathbf{x}$