Question

if \(\sin θ=\frac{11}{15}\) then the value of (sec θ - tan θ) is:
1. \(\frac{\sqrt{26}}{13}\)
2. \(\frac{1}{\sqrt{26}}\)
3. \(\frac{4}{\sqrt{26}}\)
4. \(\frac{2\sqrt{26}}{13}\)

Answer 1

Correct Answer - Option 1 : \(\frac{\sqrt{26}}{13}\)

Given:

sinθ = 11/15

Formula used:

b² = √h² – p²

sinθ = p/h

secθ = h/b

tanθ = p/b

Calculation:

We know that,

sinθ = p/h = 11/15

b² = √h² – p²

⇒ b² = √(15)² – (11)²

⇒ b² = √225 – 121

⇒ b² = √104

⇒ b = 2√26

secθ = h/b = 15/2√26

tanθ = p/b = 11/2√26

 (sec θ –  tan θ) = (15/2√26 – 11/2√26)

⇒ 4/2√26

⇒ 2/√26

Multiplying by √26 both sides we get,

⇒ (2/√26 × √26/√26)

⇒ (2√26)/26

⇒ √26/13

∴ Required value is \(\frac{\sqrt{26}}{13}\)