tanA=ntanB and sinA=m sinB then Prove that cos squareA=m square-1/n square-1
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Substitute the value of CosecB and CotB from equation 1 and equation 2(m/SinA)^2 - (n/TanA)^2 = 1m^2/Sin^2A - n^2 Cos^2A/Sin^2A = 1 (As Tan^2A = Sin^2A/Cos^2A)m^2 - n^2 Cos^2A = Sin^2Am^2 - n^2 Cos^2A = 1 - Cos^2A (Sin^2A = 1 - Cos^2A)n^2Cos^2A - Cos^2A = m^2 - 1Cos^2A (n^2 - 1) = m^2 - 1Cos^2A = (m^2 - 1) / (n^2 - 1)
Hence proved.
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