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If cos x = \(\sqrt{\frac{a}{b}}\) find cosec x

Mathematics
JAMB 1991

If cos x = \(\sqrt{\frac{a}{b}}\) find cosec 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 Answer: Option C
Explanation

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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