Question

1 + cos²2x= 2(cos⁴x + sin⁴x)​

Answer 1

$\cos2x = \cos^{2}x- \sin^{2}x$

$\cos ^{2} 2x = (\cos^{2}x- \sin^{2}x)^{2}$

$\cos ^{2} 2x = \cos^{4}x + \sin^{4}x - 2\cos^{2}x\sin^{2}x$

$1 + \cos ^{2} 2x = \cos^{4}x + \sin^{4}x - 2\cos^{2}x\sin^{2}x + 1$

$1 + \cos ^{2} 2x = \cos^{4}x + \sin^{4}x - \cos^{2}x\sin^{2}x + \cos^{2}x + \sin^{2}x - \cos^{2}x\sin^{2}x$