If sin x + cos x = √3 cos x, then the value of cot x is:1. \(\frac{

1.	If sin x + cos x = √3 cos x, then the value of cot x is:1. \(\frac{{\sqrt 3 + 1}}{2}\)2. √33. 14. \(\frac{{\sqrt 3 -1}}{2}\)
Answer» Correct Answer - Option 1 : \(\frac{{\sqrt 3 + 1}}{2}\) Given: sin x + cos x = √3 cos x Concept used: Rationalization method used. Formula used: Tanθ = Sinθ/Cosθ a²– b² = (a + b) × (a – b) Calculation: sin x + cos x = √3 cos x ⇒ (sin x + cos x)/cos x = √3 ⇒ (sin x/cos x + cos x/cos x ) = √3 ⇒ tan x + 1 = √3 ⇒ tan x = √3 – 1 ⇒ 1/cot x = √3 – 1 ⇒ cot x = 1/(√3 – 1) ⇒ cot x = (√3 + 1)/[(√3 – 1) × (√3 + 1)] ⇒ cot x = (√3 + 1)/[(√3)² – 1] ⇒ cot x = (√3 + 1)/(3 – 1) ⇒ cot x = (√3 + 1)/2 ∴ The value of cot x is (√3 + 1)/2.

If sin x + cos x = √3 cos x, then the value of cot x is:1. \(\frac{{\sqrt 3 + 1}}{2}\)2. √33. 14. \(\frac{{\sqrt 3 -1}}{2}\)

Answer» Correct Answer - Option 1 : \(\frac{{\sqrt 3 + 1}}{2}\)

Given:

sin x + cos x = √3 cos x

Concept used:

Rationalization method used.

Formula used:

Tanθ = Sinθ/Cosθ

a²– b² = (a + b) × (a – b)

Calculation:

sin x + cos x = √3 cos x

⇒ (sin x + cos x)/cos x = √3

⇒ (sin x/cos x + cos x/cos x ) = √3

⇒ tan x + 1 = √3

⇒ tan x = √3 – 1

⇒ 1/cot x = √3 – 1

⇒ cot x = 1/(√3 – 1)

⇒ cot x = (√3 + 1)/[(√3 – 1) × (√3 + 1)]

⇒ cot x = (√3 + 1)/[(√3)² – 1]

⇒ cot x = (√3 + 1)/(3 – 1)

⇒ cot x = (√3 + 1)/2

∴ The value of cot x is (√3 + 1)/2.