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Geometry Level 2

10 ( sec α + tan α ) csc α cot α \large \dfrac{10(\sec\alpha + \tan \alpha)}{\csc\alpha - \cot\alpha }

If sin α = 5 13 \sin \alpha = \dfrac5{13} , and π 2 < α < π \dfrac\pi2 < \alpha < \pi , find the value of the expression above.

3 -3 5 -4

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2 solutions

Jack Cornish
Jan 12, 2016

The desired expression is equivalent to 10 ( 13 12 + 5 13 12 13 13 5 1 5 13 12 13 ) = 3 10*\left(\dfrac{\dfrac{13}{-12}+\dfrac{\dfrac{5}{13}}{\dfrac{-12}{13}}}{\dfrac{13}{5}-\dfrac{1}{\dfrac{\dfrac{5}{13}}{\dfrac{-12}{13}}}} \right) = -3 .

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