What is the value of sin^2(45)+8cos^2(30) ?

The value of sin^2(45)+8cos^2(30) is 13/2

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sin^2(45)+8cos^2(30)

sin^{2} (4 5^{\circ}) + 8 cos^{2} (3 0^{\circ})

\frac{13}{2}

Solution steps

sin^{2} (4 5^{\circ}) + 8 cos^{2} (3 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

= (\frac{2}{2})^{2} + 8 (\frac{3}{2})^{2}

Simplify

(\frac{2}{2})^{2} + 8 (\frac{3}{2})^{2} : \frac{13}{2}

= \frac{13}{2}

cos (0.6593)

tan (3 0^{\circ}) tan (6 0^{\circ})

sin (\frac{π}{4} + \frac{π}{4})

arccos (\frac{30}{40})

36 \cdot sin (6 0^{\circ})

What is the value of sin^2(45)+8cos^2(30) ?
The value of sin^2(45)+8cos^2(30) is 13/2