What is the value of cos^2(60)+sin^2(45) ?

The value of cos^2(60)+sin^2(45) is 3/4

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cos^2(60)+sin^2(45)

cos^{2} (6 0^{\circ}) + sin^{2} (4 5^{\circ})

\frac{3}{4}

Solution steps

cos^{2} (6 0^{\circ}) + sin^{2} (4 5^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

= (\frac{1}{2})^{2} + (\frac{2}{2})^{2}

Simplify

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

= \frac{3}{4}

- \frac{1}{2} sin (\frac{π}{2}) - 4 cos (π)

tan (\frac{5 π}{2}) - 2 π

\frac{1}{cos ^{2} ( \frac{3 π}{4} )}

sin (\frac{1}{2})

sec^{2} (2 \cdot \frac{π}{6})

What is the value of cos^2(60)+sin^2(45) ?
The value of cos^2(60)+sin^2(45) is 3/4