Question

Find the value of
$4({\sin }^4{30}^o+{\cos }^4{60}^o)-3({\sin }^2{45}^o-2{\cos }^2{45}^o)$

• A. $1$
• B. $2$
• C. $0$
• D. $3$

Answer 1

The correct option is B $2$

$4(si{n}^4{30}^0+co{s}^4{60}^0)-3(si{n}^2{45}^0-2co{s}^2{45}^0)$

Put the value of $\sin$ and $\cos$ we get:

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

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

=$\frac{1}{2}+\frac{3}{2}=2$