Question

cot²θ[(cosec θ – cot θ)(tan θ + sin θ)]sec θ is equal to –
1. 1
2. -1
3. 2
4. -2

Answer 1

Correct Answer - Option 1 : 1

GIVEN:

cot²θ[(cosec θ – cot θ)(tan θ + sin θ)]sec θ

FORMULA USED:

1 – cos²x = sin²x

1 – sin²x = cos²x

CALCULATION:

cot²θ[(cosec θ – cot θ)(tan θ + sin θ)]sec θ

⇒ cot²θ[(1/sin θ – cos θ/sin θ)(sin θ/cos θ + sin θ)]sec θ

⇒ cot²θ[(1 – cos θ)(1 + cos θ)]sec θ/(cos θ)

⇒ cot²θ[1 – cos²θ]sec θ/(cos θ)

⇒ cot²θ(sin²θ)/(cos²θ)

⇒ cot²θ × tan²θ

⇒ 1