If √3sinθ = 3 cosθ then fin the value of sec2θ – 2?1. 52. 23. 7

1.	If √3sinθ = 3 cosθ then fin the value of sec2θ – 2?1. 52. 23. 74. 9
Answer» Correct Answer - Option 2 : 2 Given: The given condition is √3sinθ = 3 cosθ Formula Used: Basic concept of trigonometric ratio and identities We know that tanθ = sinθ/cosθ tan60° = √3 and Sec60° = 2 Calculation: By rearranging the expression ∴ √3sinθ = 3 cosθ ⇒ Sinθ/cosθ = 3/√3 ⇒ tanθ = 3/√3 Now, by rationalizing the denominator ∴ tanθ = √3 Also, tan60° = √3 ∴ tanθ = tan60° ⇒ θ = 60° Now, the value of sec²θ – 2 ∴ sec²(60°) – 2 ⇒ 4 – 2 = 2 Hence, option (2) is correct

If √3sinθ = 3 cosθ then fin the value of sec2θ – 2?1. 52. 23. 74. 9

Answer» Correct Answer - Option 2 : 2

Given:

The given condition is √3sinθ = 3 cosθ

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

tanθ = sinθ/cosθ

tan60° = √3 and Sec60° = 2

Calculation:

By rearranging the expression

∴ √3sinθ = 3 cosθ

⇒ Sinθ/cosθ = 3/√3

⇒ tanθ = 3/√3

Now, by rationalizing the denominator

∴ tanθ = √3

Also, tan60° = √3

∴ tanθ = tan60°

⇒ θ = 60°

Now, the value of sec²θ – 2

∴ sec²(60°) – 2

⇒ 4 – 2 = 2

Hence, option (2) is correct