Is cos(-pi/4)=sin(pi/4) ?

The answer to whether cos(-pi/4)=sin(pi/4) is True

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prove cos(-pi/4)=sin(pi/4)

prove

cos (- \frac{π}{4}) = sin (\frac{π}{4})

True

Solution steps

cos (- \frac{π}{4}) = sin (\frac{π}{4})

Manipulating left side

cos (- \frac{π}{4})

Use the negative angle identity:

cos (- x) = cos (x)

= cos (\frac{π}{4})

Simplify

= \frac{2}{2}

Manipulating right side

sin (\frac{π}{4})

Simplify

= \frac{2}{2}

We showed that the two sides could take the same form

\Rightarrow True

sin (u) cos (u) = \frac{1}{2} sin (2 u)

(cot (x) - 1)^{2} = csc^{2} (x) - 2 cot (x)

cot (2 θ) = \frac{( cot ^{2} ( θ ) - 1 )}{2 cot ( θ )}

cos^{2} (θ) = (\frac{1}{sec ^{2} ( θ )})

\frac{1}{tan ( θ )} = cot (θ)