If cos x sqrt frac a b find coses x - JAMB Mathematics 1991 Question
If cos x = (\sqrt{\frac{a}{b}}) find coses x
A
\(\frac{b}{\sqrt{b - a}}\)
B
\(\sqrt{\frac{b}{a}}\)
C
\(\sqrt{\frac{b}{b - a}}\)
D
\(\sqrt{\frac{b - a}{a}}\)
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Correct Option: C
cosx = (\sqrt{\frac{a}{b}})
y2 + (\sqrt{(a)^2}) = (\sqrt{(b)^2}) by pythagoras
y2 = b - a
∴ y = b - a
cosec x = (\frac{1}{sin x}) = (\frac{1}{y})
(\frac{b}{y}) = (\frac{\sqrt{b}}{\sqrt{b - a}})
= (\sqrt{\frac{b}{b - a}})
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