Question

PLEASE SOLVE IT FAST

BEST ANS . WILL BE MARKED AS BRAINLIST​

Answer 1

$le t\: sinx \: be \: s \: and \: cosx \: be \: c$

$(s + c) {}^{4} = (1 + sin2x) {}^{2}$

$= 1 + sin {}^{2} 2x + 2sin2x$

$(s - c) {}^{2} = 1 - sin2x$

${s}^{6} + {c}^{6} = 1 - 3 {s}^{2} {c}^{2}$

LHS =

$6(s + c) {}^{4} + 12(s - c) {}^{2} + 8( {s}^{6} + {c}^{6)}$

$= 6(1 + sin {2x}^{2} + 2sin2x) + 12(1 - sin2x) + 8(1 - 3 {s}^{2} c {}^{2} )$

$= 6 + 6 {sin}^{2} 2x + 12sin2x + 12 - 12si2x + 8 - 24 {s}^{2} {c}^{2}$

$= 26$