Is cos(45-x)=cos(x-45) ?

The answer to whether cos(45-x)=cos(x-45) is True

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prove cos(45-x)=cos(x-45)

prove

cos (4 5^{\circ} - x) = cos (x - 4 5^{\circ})

True

Solution steps

cos (4 5^{\circ} - x) = cos (x - 4 5^{\circ})

Manipulating left side

cos (4 5^{\circ} - x)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (- 4 5^{\circ} + x)

= cos (x - 4 5^{\circ})

We showed that the two sides could take the same form

\Rightarrow True

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