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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Updated on: 10-Oct-2022

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