Question

if tan theta + cot theta/tan theta- cot theta =2 find theta​

Answer 1

We are given the following equation,

→ (tan∅ + cot∅)/(tan∅ - cot∅) = 2

Since cot∅ =1/ tan∅, hence

→ (tan∅ + 1/tan∅)/(tan∅ - 1/tan∅) = 2

→ (tan²∅ + 1)/tan∅/(tan²∅ - 1)/tan∅ = 2

→ (tan²∅ + 1)/(tan²∅ - 1) = 2

→ tan²∅ + 1 = 2 tan²∅ - 2

→ 0 = tan²∅ - 3

→ 3 = (tan∅)²

→ √3 = tan∅

→ √3 = tan60°

→ tan∅ = tan60° → ∅ = 60°

Hence the required answer is 60°.