No products in the cart.

Sin theta+2cos theta=1 prove that 2sin …

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Sin theta+2cos theta=1 prove that 2sin theta-cos theta=2
  • 1 answers

Sia ? 5 years, 11 months ago

Given, sin θ + 2 cos θ = 1 

On squaring both sides, we get

(sinθ+2cosθ)2=1

sin2θ+4cos2θ+4sinθcosθ=1

⇒ 1 – cos2 θ + 4 (1 – sin2 θ) + 4 sin θ cos θ = 1 [sin2θ+cos2θ=1]

⇒ 1 – cos2 θ + 4 – 4 sin2 θ + 4 sin θ cos θ = 1

⇒ –cos2 θ – 4 sin2 θ + 4 sin θ cos θ = –4

(cos2θ+4sin2θ4sinθcosθ)=4

⇒ cos2 θ + 4 sin2 θ – 4 sin θ cos θ = 4

⇒ (cos θ)2 + (2 sin θ)2 – 2(cos θ) (2 sin θ) = 4

⇒ (2 sin θ – cos θ)2 = 22

2 sin θ – cos θ = 2

Hence proved.

http://mycbseguide.com/examin8/

Related Questions

(A + B )²
  • 1 answers
sin60° cos 30°+ cos60° sin 30°
  • 2 answers
X-y=5
  • 1 answers
Venu Gopal has twice
  • 0 answers
Find the nature of quadratic equation x^2 +x -5 =0
  • 0 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Download myCBSEguide App