Question

The value of $4({\sin }^4{30}^{\circ }+{\cos }^4{30}^{\circ })-3({\cos }^2{45}^{\circ }+{\sin }^2{90}^{\circ })$ is:

• A. $-\frac{1}{2}$
• B. $-2$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $-2$

Given: $4({\sin }^{4}30°+{\cos }^{4}30°)-3({\cos }^{2}45°+{\sin }^{2}90°)$

$=4({\left(\frac{1}{2}\right)}^4+{\left(\frac{\sqrt{3}}{2}\right)}^4)-3({\left(\frac{1}{\sqrt{2}}\right)}^2+1^2)$

$=4(\frac{1}{16}+\frac{9}{16})-3(\frac{1}{2}+1)$

$=(4\times \frac{10}{16})-(3\times \frac{3}{2})$

$=\frac{5}{2}-\frac{9}{2}$

$=\frac{-4}{2}$

$=-2$

Hence, the answer is $-2.$