What is the value of cos^2((5pi)/4) ?

The value of cos^2((5pi)/4) is 1/2

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cos^2((5pi)/4)

cos^{2} (\frac{5 π}{4})

\frac{1}{2}

Solution steps

cos^{2} (\frac{5 π}{4})

Rewrite using trig identities:

\frac{1 + cos ( \frac{π}{2} )}{2}

= \frac{1 + cos ( \frac{π}{2} )}{2}

Use the following trivial identity:

cos (\frac{π}{2}) = 0

= \frac{1 + 0}{2}

Simplify

= \frac{1}{2}

3 tan (4 5^{\circ}) + csc (3 0^{\circ}) cos (6 0^{\circ})

\frac{sin ( 4 7 ^{\circ} ) + cos ( 1 7 ^{\circ} )}{cos ( 4 7 ^{\circ} ) + sin ( 1 7 ^{\circ} )}

10 cos (7 5^{\circ}) cos (1 5^{\circ})

cos^{2} (\frac{5 π}{6}) - 2 sin (\frac{5 π}{6})

- sin (27 0^{\circ})