Question

$2{\sin }^2{54}^{\circ }-2{\cos }^2{36}^{\circ }+4{\sin }^2{30}^{\circ }$

Answer 1

$2{\sin }^2{54}^{\circ }-2{\cos }^2{36}^{\circ }+4{\sin }^2{30}^{\circ }$
= $2{\sin }^2(90-36{)}^{\circ }-2{\cos }^2{36}^{\circ }+4{\sin }^2{30}^{\circ }$
= $2{\cos }^2{36}^{\circ }-2{\cos }^2{36}^{\circ }+4{\sin }^2{30}^{\circ }$
= $4{\sin }^2{30}^{\circ }$
= $4(\frac{1}{2}{)}^2$
= $4\times \frac{1}{4}$
= $1$