Question

Find the value of $2[si{n}^6{735}^{\circ }+co{s}^6{735}^{\circ }]$ -3[$si{n}^4{735}^{\circ }+co{s}^4{735}^{\circ }$]+1.

Answer 1

$2(si{n}^6{735}^{\circ }+co{s}^6{735}^{\circ })-3(si{n}^4{735}^{\circ }+co{s}^4{735}^{\circ })+1$
$sin{735}^{\circ }=sin{15}^{\circ }$
$cos{735}^{\circ }=cos{15}^{\circ }$
$A=2(si{n}^6{15}^{\circ }+co{s}^6{15}^{\circ })-3(si{n}^4{15}^{\circ }+co{s}^4{15}^{\circ })+1$
$Letsi{n}^6{15}^{\circ }+co{s}^6{15}^{\circ }$
$=(si{n}^{2}15{)}^3+(co{s}^2{15}^{\circ }{)}^3$
$=(si{n}^2{15}^{\circ }+co{s}^2{15}^{\circ })(si{n}^4{15}^{\circ }+co{s}^4{15}^{\circ }-si{n}^{2}15co{s}^{2}15)$
$A=2\left(1\right)(si{n}^4{15}^{\circ }+co{s}^4{15}^{\circ }-si{n}^{2}15co{s}^{2}15)-3(si{n}^{4}15+co{s}^{41})$
$=(-si{n}^4{15}^{\circ }-co{s}^4{15}^{\circ }-2si{n}^5{15}^{\circ }co{s}^{2}15)+1$
$=-(si{n}^{2}15+co{s}^2{15}^{\circ }{)}^2+1$
= -1 + 1 = 0