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

The value of 3sin^2(45)+4cos^2(45) is 7/2

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3sin^2(45)+4cos^2(45)

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

\frac{7}{2}

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

= 3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2}

Simplify

3 (\frac{2}{2})^{2} + 4 (\frac{2}{2})^{2} : \frac{7}{2}

= \frac{7}{2}

sin (\frac{π}{5}) cos (\frac{2 π}{15}) + cos (\frac{π}{5}) sin (\frac{2 π}{15})

\frac{0.02}{tan ( 20 7 ^{\circ} )}

e^{\frac{3 π}{2}} sin (\frac{3 π}{2})

sec (3 1^{\circ})

arccos (\frac{- 4}{21})

What is the value of 3sin^2(45)+4cos^2(45) ?
The value of 3sin^2(45)+4cos^2(45) is 7/2