If cosec = √5 and θ is less than 90°.

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 OP² = OM² + PM²

(√5)² = OM² + 1²

⇒ 5 = OM² + 1

⇒ OM² = 5 – 1

⇒ OM² = 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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