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Given that cos x = 1/r, express tan x in terms of r

A. 1/✓r

B. ✓r

C. ✓r² + 1

D. ✓r² - 1

**Comments**

D

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cosx = 1/r

But from trigonometry, cosx = adj/hyp

Therefore,

adj = 1

hyp = r

tanx = opp/adj

From pythagoras theorem,

hyp^{2} = opp^{2} + adj^{2}

opp = ✓hyp^{2} - adj^{2}

opp = ✓r^{2} - 1^{2}

opp = ✓r^{2} - 1

tanx = (✓r^{2} - 1)/1

tanx = ✓r^{2} - 1

**Ans D**

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