Question

Prove that $\sin (\pi -x)=\sin \left(x\right)$

Answer 1

To prove $\sin (\pi -x)=\sin \left(x\right)$ we will use sine Subtraction formula.

$\sin (a-b)=\sin \left(a\right)\cos \left(b\right)-\cos \left(a\right)\sin \left(b\right)$

Let us assume $a=\pi andb=x$

$\sin (\pi -x)=\sin \left(\pi \right)\cos \left(x\right)-\cos \left(\pi \right)\sin \left(x\right)$

$$\begin{gathered} =0\times cos\left(x\right)-(-1)\times sin(x) \\ =0+\sin \left(x\right) \\ =sin(x) \end{gathered}$$

Therefore, LHS = RHS

Hence, Proved.