How do you prove cos (pi - x) = - cosx?

To prove

cos(∏-x)= – cos X

Proof

We can evaluate cos(∏-x) using the trigonometric identity

cos (A – B) = cos A cos B + sin A cos B

Hence,

cos(∏-x)= cos π cos x + sin π sin x

Now will substitute the known values.

We know that cos π =-1 and sin π=0

Therefore

cos(∏-x)= (-1) cos x + sin π sin x

cos(∏-x)= -cosx + 0

cos(∏-x)= – cos X

= RHS

Hence proved

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