Question & Answer » Mathematics Questions » Prove that sin(pi-x) = sin(x)

Prove that sin(pi-x) = sin(x)

Let us follow the given 

Sin(pi-x)

Now, we have to prove that sin (pi–x) = sin (x)

For this, we have to imply the sine subtraction formula which is 

Sin (a-b) = sin(a) cos(b) – cos(a) sin(b) 

Moving forward assuming the a = π & b = x

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

= 0 * {cos (x)} – {-1 * sin(x)}

Now 0 – {-sin (x)}

That is equal to sin (x)

Hence proved that sin (pi-x) = sin (x) 

Answer is seemingly easy to calculate.

Time to try it out & learn it in an interesting method.