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sinA(1+sin^2A) = cos^2A
sinA(2 -cos^2A) = cos^2A
Squaring both sides,
sin^2A(4-4cos^2A +cos^4A) = cos^4A
(1-cos^2A)(4-4cos^2A +cos^4A) = cos^4A
4-4cos^2A +cos^4A-4cos^2A+4cos^4A-cos^6A = cos^4A
4 -cos^6A +4cos^4A -8cos^2A = 0
cos^6A - 4 cos^4A + 8cos^2A = 4
Hence Proved.
sinA(2 -cos^2A) = cos^2A
Squaring both sides,
sin^2A(4-4cos^2A +cos^4A) = cos^4A
(1-cos^2A)(4-4cos^2A +cos^4A) = cos^4A
4-4cos^2A +cos^4A-4cos^2A+4cos^4A-cos^6A = cos^4A
4 -cos^6A +4cos^4A -8cos^2A = 0
cos^6A - 4 cos^4A + 8cos^2A = 4
Hence Proved.
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