What is the value of 4cos^2(30)+6sin^2(30) ?

The value of 4cos^2(30)+6sin^2(30) is 9/2

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4cos^2(30)+6sin^2(30)

4 cos^{2} (3 0^{\circ}) + 6 sin^{2} (3 0^{\circ})

\frac{9}{2}

Solution steps

4 cos^{2} (3 0^{\circ}) + 6 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}

= 4 (\frac{3}{2})^{2} + 6 (\frac{1}{2})^{2}

Simplify

4 (\frac{3}{2})^{2} + 6 (\frac{1}{2})^{2} : \frac{9}{2}

= \frac{9}{2}

ln (sec (\frac{π}{3}) + tan (\frac{π}{3}))

cos (12 0^{\circ}) + tan^{2} (24 0^{\circ}) - 5

\frac{cos ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan (tan (\frac{5 π}{7}))

sin^{3} (1)

What is the value of 4cos^2(30)+6sin^2(30) ?
The value of 4cos^2(30)+6sin^2(30) is 9/2