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Question
If 5 cos θ = 3, evaluate : `(co secθ – cot θ)/(co secθ + cot θ)`
Solution
cos θ = `(3)/(5)`
Now
`(co secθ – cot θ)/(co secθ + cot θ) = (1/sinθ – cosθ/sinθ)/(1/ sinθ + cosθ/sinθ)`
= `((1 – cos θ)/(sin θ))/((1 + cos θ)/(sinθ))`
= `( 1 – cos θ)/(1 + cos θ)`
= `(1 – (3)/(5))/(1+(3)/(5))`
= `((2)/(5))/((8)/(5))`
= `(2)/(8)`
= `(1)/(4)`
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