if 1-sinA = tanA. prove that,sin^2A=1+cos^2A/cos^2A
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1-sinA = tanA
(1-sinA)^2 = tan^2A
1 - 2sinA + sin^2A = Tan^2A
Sin^2A = (Sin^2A/cos^2A) + 2SinA - 1
= Sin^2A + 2sinAcos^2A - cos^2A
= 1 - cos^2A + 2(1-cos^2A)cos^A - cos^2A
= 1 - cos^2A + Cos^2A(2 - 2cos^2A)
= 1 - cos^2A + 2cos^2A - 2cos^4A
= 1 + cos^2A - 2cos^4A
This is what I'm getting as RHS. I think there is an ambiguity in the question. If there is any mistake in my part kindly do post it in comment box. Thank you.
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