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