Question

If Tan θ + Sec θ = 8, then Sec θ – Tan θ value is

A) 8

B) 1/8

C) 6 

D) 64

Answer 1

Correct option is: B) \(\frac 18\)

We have Tan \(\theta\) + Sec  \(\theta\)  = 8

\(\therefore\) ( sec \(\theta\) + tan \(\theta\)) (sec \(\theta\) - tan \(\theta\)) = 8 (sec \(\theta\) - tan \(\theta\))

(on multiplying both sides by sec \(\theta\) - tan \(\theta\))

= \(sec^2\theta-tan^2 \theta\) = 8 (sec \(\theta\) - tan \(\theta\)) (\(\because\) (a+b) (a-b) = \(a^2 - b^2\))

= 8 (sec \(\theta\) - tan \(\theta\)) = 1 (\(\because\) \(sec^2\theta-tan^2 \theta\) = 1)

= sec \(\theta\) - tan \(\theta\) = \(\frac 18\) 

Answer 2

Correct option is: B) \(\frac{1}{8}\)