Question

4(sin 4 30 + cos 4 60)-3(cos 2 45-sin 2 90)

Answer 1

Solution is attached below

Answer 2

Answer:

$Value\: of \: 4(sin^{4}30+cos^{4}60)-3(cos^{2}45-sin^{2}90)$

$= 2$

Explanation:

$Value\: of \: 4(sin^{4}30+cos^{4}60)-3(cos^{2}45-sin^{2}90)$

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

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

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

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

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

$=\frac{4}{2}$

$= 2$

Therefore,

$Value\: of \: 4(sin^{4}30+cos^{4}60)-3(cos^{2}45-sin^{2}90)$

$= 2$

•••♪