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Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)

Mathematics
JAMB 1980

Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
  • A. \(\frac{1 - cos x}{sin x}\)
  • B. 1 - cos x
  • C. sin x
  • D. 1 + cos x
  • E. \(\frac{1 + cos x}{sin x}\)
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Correct Answer: Option A
Explanation
\(\sqrt{\frac{1 - cos x}{1 + cos x}}\) = a

a2 = \(\frac{1 - cosx}{1 + cosx}\)

\(\frac{1 - cosx}{1 + cosx}\) = \(\frac{1 - cosx}{1 - cosx}\)

= \(\frac{(1 - cosx)^2}{cos^2 x}\)

a2 = \(\frac{(1 - cos x)^2}{sin^2 x}\)

a = \(\frac{1 - cos x}{sin x}\)

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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts