Math, asked by vinodkumarregar587, 10 months ago

cos θ + sin θ = √2 cos θ, at cos θ - sin θ= ?
(1) √2 tan θ
(2) - √2 cos θ
(3) - √2 sin θ
(4) √2 sin θ​

Answers

Answered by Mankuthemonkey01
54

Answer

√2 sin∅

Explanation

Given

cos∅ + sin∅ = √2cos∅

Squaring both sides,

(cos∅ + sin∅)² = (√2cos∅)²

⇒ cos²∅ + sin²∅ + 2sin∅cos∅ = 2 cos²∅

⇒ 2sin∅cos∅ = 2cos²∅ - cos²∅ - sin²∅

⇒ 2sin∅cos∅ = cos²∅ - sin²∅

Now, using a² - b² = (a + b)(a - b)

⇒ 2sin∅cos∅ = (cos∅ + sin∅)(cos∅ - sin∅)

Now, we know that (cos∅ + sin∅) = √2cos∅

⇒ 2sin∅cos∅ = (√2cos∅)(cos∅ - sin∅)

⇒ cos∅ - sin∅ = 2sin∅cos∅/√2cos∅

cos∅ - sin∅ = √2sin∅

Answered by MarshmellowGirl
48

 \large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}

Attachments:
Similar questions