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

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

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

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

\frac{9}{4}

Solution steps

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

= 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}

sin (73 5^{\circ})

\frac{cos ^{3} ( \frac{π}{2} )}{3}

sin (3 0^{\circ}) + csc (6 0^{\circ})

arcsin (sin (- \frac{5 π}{2}))

arctan (\frac{15}{12})

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