**If cosec = √5 and θ is less than 90°, find the value of cot θ – cos θ.**

**Answer :**

Given cosec θ = √5/1 = OP/PM

OP = √5 and PM = 1

Now OP^{2} = OM^{2} + PM^{2}

(√5)^{2} = OM^{2} + 1^{2}

⇒ 5 = OM^{2} + 1

⇒ OM^{2} = 5 – 1

⇒ OM^{2} = 4

⇒ OM = 2

Now cot θ = OM/PM

= 2/1

= 2

cos θ = OM/OP

= 2/√5

cot θ – cos θ = 2 – (2/√5)

= 2 (√5 – 1)/ √5

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