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Question
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
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Solution
Let x be, the hypotenuse
By Pythagoras we get
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
𝑥2 = 144 + 169
`x = sqrt313`
`sin theta = (AB)/(AC) = 12/sqrt313`
`cos theta = (BC)/(AC) = 13/sqrt313`
Substitute, Sin 𝜃, cos 𝜃 in equation we get
`(2 sin theta cos theta)/(cos^2 theta - sin^2 theta) => (2 xx 12/sqrt313 xx 13/sqrt313)/(169/313 - 144/313)`
`= (312/313)/(25/313) = 312/25`
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