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If `Tan Theta = 12/13` Find `(2 Sin Theta Cos Theta)/(Cos^2 Theta - Sin^2 Theta)` - Mathematics

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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.1 | Q 20 | Page 25
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