Question

The value of
$4(si{n}^4{30}^0+co{s}^4{60}^0)(co{s}^2{45}^0-si{n}^2{90}^0)+ta{n}^4{45}^0-co{t}^2{45}^0$ is

• A. $0$
• B. $1$
• C. $-\frac{1}{4}$
• D. -2

Answer 1

The correct option is C $-\frac{1}{4}$

$4(si{n}^4{30}^0+co{s}^4{60}^0)(co{s}^2{45}^0-si{n}^2{90}^0)+ta{n}^4{45}^0-co{t}^2{45}^0$
$=4[{\left(\frac{1}{2}\right)}^4+{\left(\frac{1}{2}\right)}^4][{\left(\frac{1}{\sqrt{2}}\right)}^2-1]+{\left(1\right)}^4-{\left(1\right)}^4=4\left(\frac{1}{8}\right)(-\frac{1}{2})+0=-\frac{1}{4}$