. If cosec θ - cot θ is = p then the value of


If cosec θ - cot θ = p, then the value of Trigonometry is

A.cos θ

B.– cos θ

C.sin θ

D.– sin θ

Best Answer

Correct Option is : B

Solution :

We have cosec θ – cot θ = p

Trigonometry

⇒ p × sin θ = 1 – cos θ

Squaring,

⇒ p2 × sin2 θ = (1 – cos θ)2

⇒ p2 × (1 – cos2 θ) = (1 – cos θ)2

⇒ p2 × (1 – cos θ) × (1 + cos θ) = (1 – cos θ)2

⇒ p2 × (1 + cos θ) = (1 – cos θ)

⇒ p2 + p2 cos θ = 1 – cos θ

⇒ p2 – 1 = - cos θ – p2cos θ

⇒ p2 – 1 = -cos θ × (p2 + 1)

Trigonometry

Hence, B is the correct answer.

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