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Question

How do you verify cos180°=-1?


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Solution

Verify cos180°=-1

180° can be rewritten as 180°=90°+90°.

Now, cos(A+B)=cos(A)·cos(B)-sin(A)·sin(B).

Thus, cos180°=cos90°+90°.

cos180°=cos90°·cos90°-sin90°·sin90°cos180°=0×0-1×1cos180°=0-1cos180°=-1

Therefore, it is verified that cos180°=-1.


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