Question

solve: 2 tan theta - cot theta
= -1​

Answer 1

Given

2tan∅ - cot∅ = - 1

Solution

2tan∅ - cot∅ = -1

We know that cot∅ = 1/tan∅

→ 2tan∅ - 1/tan∅ = -1

Taking LCM,

→ (2tan²∅ - 1)/tan∅ = -1

Cross multiplying

→ 2tan²∅ - 1 = - tan∅

→ 2tan²∅ + tan∅ - 1 = 0

→ 2tan²∅ + 2tan∅ - tan∅ - 1 = 0

→ 2tan∅(tan∅ + 1) - 1(tan∅ + 1) = 0

→ (2tan∅ - 1)(tan∅ + 1) = 0

→ tan∅ = 1/2 or tan∅ = -1

Answer 2

Step-by-step explanation:

Given:

• 2 tanθ – cotθ = –1

To prove: L.H.S = R.H.S

Solution: We know that Cotθ = 1/tanθ

†Putting Values†

→ 2 tanθ – 1/tanθ = –1

Taking LCM, We get

→ (2 tan²θ –1)/tanθ = –1

→ 2 tan²θ – 1 = –tanθ ( Cross multiply)

→ 2 tan²θ + tanθ – 1 = 0

→ 2 tan²θ (tanθ + 1) – (tanθ + 1) = 0

→ (tanθ – 1) (tanθ + 1) = 0

Therefore, Tanθ = 1/2 or Tanθ = –1