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Question

How do you simplify cos(x+π)?


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Solution

Solve for the required value

We can evaluatecos(π+x) using the trigonometric identity

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

So we get,

cos(π+x)=cosπcosxsinπsinx

We know that cosπ=-1 and sinπ=0

Therefore

cos(π+x)=(-1)cosx0sinxcos(π+x)=-cosx+0cos(π+x)=cosx,

Hence, the required answer is cos(π+x)=cosx


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