What is the value of cos^2((5pi)/4)-sin^2((2pi)/3) ?

The value of cos^2((5pi)/4)-sin^2((2pi)/3) is -1/4

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cos^2((5pi)/4)-sin^2((2pi)/3)

cos^{2} (\frac{5 π}{4}) - sin^{2} (\frac{2 π}{3})

- \frac{1}{4}

Solution steps

cos^{2} (\frac{5 π}{4}) - sin^{2} (\frac{2 π}{3})

Rewrite using trig identities:

cos^{2} (\frac{5 π}{4}) = \frac{1 + cos ( \frac{π}{2} )}{2}

= \frac{1 + cos ( \frac{π}{2} )}{2} - sin^{2} (\frac{2 π}{3})

\frac{1 + cos ( \frac{π}{2} )}{2} - sin^{2} (\frac{2 π}{3}) = \frac{1 + cos ( \frac{π}{2} ) - 2 sin ^{2} ( \frac{2 π}{3} )}{2}

= \frac{1 + cos ( \frac{π}{2} ) - 2 sin ^{2} ( \frac{2 π}{3} )}{2}

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= \frac{1 + 0 - 2 ( \frac{3}{2} ) ^{2}}{2}

Simplify

\frac{1 + 0 - 2 ( \frac{3}{2} ) ^{2}}{2} : - \frac{1}{4}

= - \frac{1}{4}

50 sin (5 3^{\circ})

arcsin (2 sin (3 0^{\circ}))

tan^{2} (62. 5^{\circ})

- 2 cos (2 \cdot 0)

arctan (- 3.25)

What is the value of cos^2((5pi)/4)-sin^2((2pi)/3) ?
The value of cos^2((5pi)/4)-sin^2((2pi)/3) is -1/4