This question is taken from trigonometry topic trigonometric identities in which we have given that cotθ=1/√3, we have been asked to find the value of (1-cos²θ)/(2-sin²θ) using trigonometric formulas

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 13C, question no 22

cotθ=1/√3

⇒cotθ=cot60°

⇒θ=60°

∴(1-cos²θ)/(2-sin²θ)

Putting the value of θ we get,

=(1-cos²60°)/(2-sin²60°)

=[1-(1/2)²]/[2-(√3/2)²]

=(1-1/4)/(2-3/4)

=(4-1)/4/(8-3)/4

=3/4/5/4

=3/5