Question

sin^4 x + cos^4 x = 1÷2 (1 + 2a^2 + a^4) where a = sin x + cos x

Answer 1

$( \sin(x) + \cos(x) ) {}^{2} = {sin}^{2}x + {cos}^{2} x+ 2sinxcosx \\ {a}^{2} = 1 + sin2x \\ sin2x = {a}^{2} - 1..............(1) \\ now \\ ( {sin}^{2} x + {cos}^{2} x) {}^{2} = {sin}^{4} x + {cos}^{4} x + 2 {sin}^{2} x {cos}^{2} x \\ {1}^{2} = {sin}^{4} x + {cos}^{4} x + (1 \div 2) {(sin2x)}^{2} \\ {sin}^{4} x + {cos}^{4} = 1 - (1 \div 2)( {a}^{2} - 1) {}^{2} ...(from(1))$
here it is proved.... mark it brainliest if helped