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Question

How is cos(-x)=cosx?


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Solution

Prove the given identity:

The given expression is, LHS=cos-x

cos-x=sin90--x ...[cosx=sin90°-x]

=sin90°+x

=sin90°cosx+cos90°sinx ...[sina+b=sinacosb+cosasinb]

=cosx+0 ...[sin90°=1;cos90°=0°]

=cosx

=RHS

Hence, the given relation cos(-x)=cosx has been proved.


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