Question

If cosec theta =2 and cot theta = root 3 p then find the value of p

Answer 1

There are two methods through which we can solve this question.

METHOD 1 - Easy to solve

This method uses (Cosec² θ - Cot² θ = 1) identity-

Cosec θ = 2

Cot θ = √3p

   Cosec² θ - Cot² θ = 1

⇒2² - √3p² = 1

⇒ 4 - 3p² = 1

⇒ 3p² = 4 - 1

⇒ 3p² = 3

⇒ P² = 3/3

⇒ p² = 1

⇒ p = √1 = 1 unit

METHOD 2 - Easy to understand

This method uses Pythagoras Theorem -

Cosec θ = 2/1 = H/P

Cot θ = √3/1 = √3p/1

By Pythagoras Theorem

    AC² = AB² + BC²

⇒ 2² = 1² + √3p²

⇒ 4 = 1 + 3p²

⇒ 3p² = 4 - 1

⇒ 3p² = 3

⇒ p² = 3/3 = 1

⇒ p = √1 = 1 unit

Mark answer as the brainliest.