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Given that cos xo = \(\frac{1}{r}\), express tan x in terms of r

Mathematics
WAEC 2011

Given that cos xo = \(\frac{1}{r}\), express tan x in terms of r
  • A. \(\frac{1}{\sqrt{r}}\)
  • B. \(\sqrt{r}\)
  • C. \(\sqrt{r^2 + 1}\)
  • D. \(\sqrt{r^2 - 1}\)
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Correct Answer: Option D
Explanation
cos xo = \(\frac{1}{r}\); \(\sqrt{r^2 - 1}\)

By Pythagoras r2 = 12 + x2 - 1

x = \(\sqrt{r^2 - 1}\)

tan xo = \(\sqrt{r^2 - 1}\)

= \(\sqrt{r^2 - 1}\)

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