Question

sin²theta +cos⁴theta =cos²theta +sin⁴theta​

Answer 1

$sin ^{2} \: θ \: + \cos ^{4} θ = cos ^{2} θ + sin ^{4} θ$

$l.h.s = sin^{2} θ + cos^{4} θ = (1 - cos ^{2} θ) + cos ^{4} θ$

$cos ^{4} θ - cos^{2} θ + 1$

$1 - sin^{2} θ \: cos ^{2} θ$

$now \: r.h.s. = cos^{2} θ + sin ^{4} θ$

$(1 - sin ^{2} θ) + sin ^{4} θ$

$sin ^{2} θ( - cos ^{2} θ) + 1$

$1 - sin ^{2} θ \: cos ^{2} θ$

L.H.S.=R.H.S

hope it will help you....