How do you simplify cos(x + pi)?

We need to evaluate cos(∏+x)

Solution

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

cos(A+B)=cos(A)⋅cos(B)−sin(A)⋅sin(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

Answer

cos(∏+x)= – cos x

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