If tanθ =12/13, Evaluate (2sinθ cosθ)/(cos²θ -sin²θ)
tanθ =12/13 = opp/adj
Given (2sinθ cosθ)/(cos²θ -sin²θ)
Dividing numerator and denominator by cos²θ
(2sinθ cosθ)/(cos²θ -sin²θ)
= (2sinθ cosθ)/cos²θ/(cos²θ/cos²θ -sin²θ/cos²θ)
= 2tanθ/(1 - tan²θ)
Substituting tanθ = 12/13
= 2 x 12/13 / (1 - [12/13]^2)
= 24/13 / (169-144)/(169)
= 24/13 / 25/169
= 24/13 x 169/25
= 24 x13/25 = 312/25 Ans
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