What is the value of 2cos^2(30)+3sin^2(30) ?

The value of 2cos^2(30)+3sin^2(30) is 9/4

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2cos^2(30)+3sin^2(30)

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

\frac{9}{4}

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

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

Simplify

2 (\frac{3}{2})^{2} + 3 (\frac{1}{2})^{2} : \frac{9}{4}

= \frac{9}{4}

4 tan^{2} (6 0^{\circ})

10 cos (1 0^{\circ})

sin (\frac{- 3}{2})

\frac{tan ( 31 5 ^{\circ} ) - cos ( 78 0 ^{\circ} )}{tan ( - 13 5 ^{\circ} ) - sin ( 21 0 ^{\circ} )}

2 - 2 cosh (3 - 2)

What is the value of 2cos^2(30)+3sin^2(30) ?
The value of 2cos^2(30)+3sin^2(30) is 9/4