If 3 cosθ + 4 sinθ = 5, then tanθ = ?

Home » Aptitude » Trigonometry » Question

If 3 cosθ + 4 sinθ = 5, then tanθ = ?

1. 4
  3
2. 3
  4
3. 3
  5
4. 5
  3

Correct Option: A

3 cosθ + 4 sinθ = 5
Dividing by cosθ,
3 + 4 tanθ = 5 secθ
On squaring,
9 + 16 tan²θ + 24 tanθ = 25 (1 + tan²θ)
⇒ 9 tan²θ – 24 tanθ + 16 = 0
⇒ (3 tanθ – 4)2 = 0
⇒ 3 tanθ = 4

⇒ tanθ =	4
	3