But the table don't show 333

Geometry Level 3

cot ⁡ ( 33 3 ∘ ) sec ⁡ 2 ( 33 3 ∘ ) − 1 = ? \large \cot(333^\circ) \sqrt{\sec^2(333^\circ) - 1} = \ ?

1 2 \frac12 -1 1 None of these choices

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Raunak Bele by Raunak Bele , 21, India

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1 solution

Alex Li
Jun 17, 2015

Because tan ⁡ ( 33 3 ∘ ) \tan(333^\circ) is negative, we have sec ⁡ 2 33 3 ∘ − 1 = tan ⁡ 2 33 3 ∘ = − tan ⁡ 33 3 ∘ \sqrt{\sec^2{333^\circ}-1}=\sqrt{\tan^2{333^\circ}}=-\tan{333^\circ} . This, the expression evaluates as − tan ⁡ 33 3 ∘ × 1 tan ⁡ 33 3 ∘ = − 1 -\tan{333^\circ}\times\frac{1}{\tan{333^\circ}}=\boxed{-1} .

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