Prove that sin (π - x)  = sin (x).

Sine is one of the primary functions of trigonometry. To prove this, we will use trigonometric identity.

Answer: Hence proved that sin (π - x)  = sin (x)

Let's prove.

Explanation:

Given that LHS = sin (π - x) 

By using trigonometric identity: sin (A - B) = sin A cos B - cos A sin B, we get

sin (π - x) = sin (π) cos (x) - cos (π) sin (x) 

As we know that sin (π) = sin 180º = 0 and cos (π) = cos 180º = - 1

sin (π - x) = 0 × cos (x) - (- 1) × sin (x) 

0 + sin (x) = RHS

Hence Proved.

Thus, sin (π - x)  = sin (x).