Question on: JAMB Mathematics - 1992
Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)
A
\(\frac{\sqrt{n^2 - m^2}{m}\)
B
\(\frac{\sqrt{(n + m)(n - m)}{n}\)
C
\(\frac{m}{\sqrt{n^2 - m^2}\)
D
\(\sqrt{\frac{n}{n^2 - m^2}}\)
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Correct Option: B
sin \(\theta\) = \(\frac{m}{n}\) x x2
= n2 - m2
x = n2 - m2 cos \(\theta\)
\(\frac{x}{n}\) = \(\frac{n^2 - m^2}{n}\)
cos \(\theta\) = \(\frac{n^2 - m^2}{n}\)
= \(\frac{(n + m)(n - m)}{n}\)
= n2 - m2
x = n2 - m2 cos \(\theta\)
\(\frac{x}{n}\) = \(\frac{n^2 - m^2}{n}\)
cos \(\theta\) = \(\frac{n^2 - m^2}{n}\)
= \(\frac{(n + m)(n - m)}{n}\)
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