UPSKILL MATH PLUS
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Learn moreIf \(\frac{cos \ \alpha}{cos \ \beta} = m\) and \(\frac{cos \ \alpha}{sin \ \beta} = n\), then prove that \((m^2 + n^2) cos^2 \ \beta = n^2\).
Consider \(\frac{cos \ \alpha}{cos \ \beta} = m\)
---- (\(1\))
Consider \(\frac{cos \ \alpha}{sin \ \beta} = n\)
---- (\(2\))
Using equation (\(2\)) in equation (\(1\)), we get:
Squaring on both sides, we have:
\(\ sin^2 \ \beta = \)\(\ cos^2 \ \beta\)
\(n^2(1 - cos^2 \ \beta) =\)
\(n^2 - n^2 \ cos^2 \ \beta = \)
\(n^2 =\) \( + n^2 \ cos^2 \ \beta\)
\(n^2 = (m^2 + n^2) cos^2 \ \beta\)
Hence, we proved.
Answer variants:
\(n \ sin \ \beta = m \ cos \ \beta\)
\(cos \ \alpha = n \ sin \ beta\)
\(m^2 \ cos^2 \ \beta\)
\(m^2 \ cos^2 \ \beta\)
\(cos \ \alpha = m \ cos \ \beta\)
\(n^2\)
\(m^2 \ cos^2 \ \beta\)
\(m^2\)
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