How do you verify the identity $cos (180 + x) = - cos x$ $cos(180+x)=-cosx$ ?

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Answer 1 · 2018-03-07T00:20:34

Use the sum in cosine identity,

$cos (A + B) = cos A cos B - sin A sin B$ $cos(A+ B) = cosAcosB - sinAsinB$ .

Thus we have:

$cos(180˚)cos(x) - sin(180˚)sinx = -cosx$

$-1(cosx) - 0(sinx)= -cosx$

$-cosx= -cosx$

$LHS = RHS$

As required.

Hopefully this helps!

How do you verify the identity cos(180+x)=-cosxcos(180+x)=−cosxcos(180+x)=-cosx?