ExamCompetition Forum Question Papers Ask A Question Mock Test Learn & Earn Sign Up Login Menu



0 vote

If 2 cos θ = 2 - sin θ, then what is the value of cos θ?

Asked on by | Votes 0 | Views: 27 | Tags: trigonometry     | quantitative aptitude     | Add Bounty

If 2 cos θ = 2 - sin θ, then what is the value of cos θ?


1). 1 or 3/5
2). 1 or -1/2
3). -1 or -1/2
4). -1 or 3/5


Share on Facebook      Share on Whatsapp       Share on Twitter




1 answers

3 vote
Answered by on | Votes 3 |

Given,

If 2 cosθ = 2 - sinθ

⇒ 2 (cosθ - 1) = -sinθ

Squaring both sides

⇒ 4 (cosθ – 1)2 = sin2θ

⇒ 4 (cosθ – 1)2 = 1 - cos2θ

⇒ 4 cos2θ + 4 - 8 cosθ = 1 - cos2θ

⇒ 5 cos2θ - 8 cosθ + 3 = 0

⇒ 5 cos2θ - 5 cosθ - 3 cosθ + 3 = 0

⇒ 5 cosθ (cosθ – 1) - 3(cosθ – 1) = 0

⇒ (5 cosθ – 3) (cosθ – 1) = 0

⇒ cosθ = 3/5, 1

Join Telegram Group




Answer This Question

Name:
Email:
Answer :
Sum of (1+1)
Submit: