If cosθ + sinθ = 2 cosθ , then prove that cosθ - sinθ = 2 sinθ

Given, cos θ + sin θ = 2 cos θ ⇒ sin θ = 2 cos θ - cos θ ⇒ sin θ = cos θ 2 - 1 ⇒ sin θ 2 - 1 = cos θ ⇒ sin θ 2 - 1 × 2 + 1 2 + 1 = cos θ ⇒ 2 + 1 sin θ 2 2 - 1 2 = cos θ ⇒ 2 + 1 sin θ = cos θ ⇒ 2 sin θ + sin θ = cos θ ⇒ 2 sin θ + sin θ = cos θ ⇒ cos θ - sin θ = 2 sin θ Hence, proved.

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Mathematics Standard 10>Chapter 6 - Trigonometry>Solved Example

Tamil Nadu Board Solutions for Chapter: Trigonometry, Exercise 8: Solved Example

Author:Tamil Nadu Board

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Trigonometry, Exercise 8: Solved Example

Attempt the free practice questions on Chapter 6: Trigonometry, Exercise 8: Solved Example with hints and solutions to strengthen your understanding. Mathematics Standard 10 solutions are prepared by Experienced Embibe Experts.