If cot theta + cosec theta equals to 5 then cos theta equals to

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Solution

$\cos e c θ + c o t θ = 5 . . . . (1) w e k n o w t h a t \cos e c^{2} θ - c o t^{2} θ = 1 (\cos e c θ + c o t θ) (\cos e c θ - c o t θ) = 1 \cos e c θ - c o t θ = \frac{1}{\cos e c θ + c o t θ} = \frac{1}{5} . . . (2) a d d e q u a t i o n 1 a n d 2 2 \cos e c θ = 5 + \frac{1}{5} = \frac{26}{5} \cos e c θ = \frac{13}{5} \sin θ = \frac{5}{13} s o \cos θ = \sqrt{1 - \sin^{2} θ} = \sqrt{1 - \frac{25}{169}} = \sqrt{\frac{144}{169}} = \frac{12}{13}$

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