Question

If \[\cos \theta = \frac{2}{3}\] find the value of \[\frac{\sec \theta - 1}{\sec \theta + 1}\]

Answer 1

Given in question: `cosθ=2/3` 

We have to find `sec θ-1/sec θ+1` 

⇒ `(sec θ-1)/(sec θ+1)= (1/cos θ-1)/(1/cosθ+1)` 

⇒ `(sec θ-1)/(sec θ+1)=(3/2-1)/(3/2+1)` 

⇒`(sec θ-1)/(sec θ+1)=(1/2 )/ (5/2)` 

⇒`(sec θ-1)/(sec θ+1)=1/5`

Hence the value of `(sec θ-1)/(sec θ+1)` is` 1/5`