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Question
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
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Solution
L.H.S. = (m2 + n2) cos2 B
= `(cos^2A/cos^2B + cos^2A/sin^2B)cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/(cos^2Bsin^2B))cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/sin^2B)`
= `(cos^2A(sin^2B + cos^2B))/sin^2B`
= `cos^2A/sin^2B`
= n2
Hence, (m2 + n2) cos2 B = n2.
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