# Explain how to find the value of \cos(-45^{\circ}) using even-odd properties.

Explain how to find the value of $$\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}$$ using even-odd properties.

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Malena
Step 1
We know the even property that
$$\displaystyle{f{{\left(-{x}\right)}}}={f{{\left({x}\right)}}}$$
And we know that cos is an even function so, 1) $$\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}={\cos{{\left({45}^{{\circ}}\right)}}}$$
Step 2
We know the value of $$\displaystyle{\cos{{\left({45}^{{\circ}}\right)}}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}.$$
Hence the value of $$\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}$$ from equation(1).