If (secθ + cosecθ)/(secθ - cosecθ) = 7 then what will be the value of secθ?

If (secθ + cosecθ)/(secθ - cosecθ) = 7 then what will be the value of secθ? Correct Answer 5/3

Given

(secθ + cosecθ)/(secθ - cosecθ) =7

Formula used

Componendo- dividend0 method

If a/b = c/d then (a + b)/(a - b) = (c + d)/(c - d)

And trigonometric ratio relation

Calculation

(secθ + cosecθ)/((secθ - cosecθ) =7/1

⇒ (secθ + cosecθ) + (secθ - cosecθ)/{ (secθ + cosecθ) - (secθ - cosecθ)} = (7 + 1)/(7 - 1)

⇒ 2secθ/2cosecθ = 8/6

⇒ tanθ = 4/3

Now, in a right angled triangle tanθ = perpendicular/base = 4/3

And secθ = hypotenuse/base = √(4² + 3²)/3 = 5/3

∴ The value of secθ will be 5/3.