Consider the following statements:I. 1/(1 + cosθ) + 1/(1 - cosθ) = 2

1.	Consider the following statements:I. 1/(1 + cosθ) + 1/(1 - cosθ) = 2cosec2θII. (1 + tan2θ)/ cosec2θ = tan2θWhich of the following statements are correct.1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2
Answer» Correct Answer - Option 3 : Both 1 and 2 Given: Two identities are given Formula Used: Basic concept of trigonometric ratio and identities We know that (a² – b²) = (a + b)(a - b) sin²θ + cos²θ = 1 1 + tan²θ = sec²θ sinθ = 1/cosecθ Calculation: The given identity is 1/(1 + cosθ) + 1/(1 - cosθ) = 2cosec²θ L.H.S. Take LCM of denominators ⇒ 2/(1 + cosθ) × (1 - cosθ) ⇒ 2/(1 - cos²θ) ⇒ 2/sin²θ ⇒ 2 cosec²θ = R.H.S. So, statement 1 is correct Now, the given identity is (1 + tan²θ)/ cosec²θ = tan²θ L.H.S. ⇒ (1 + tan²θ)/cosec²θ ⇒ sec²θ/cosec²θ ⇒ sin²θ/cos²θ ⇒ tan²θ = R.H.S. So, statement 2 is correct Hence, option (3) is correct

Consider the following statements:I. 1/(1 + cosθ) + 1/(1 - cosθ) = 2cosec2θII. (1 + tan2θ)/ cosec2θ = tan2θWhich of the following statements are correct.1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 3 : Both 1 and 2

Given:

Two identities are given

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

(a² – b²) = (a + b)(a - b)

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

sinθ = 1/cosecθ

Calculation:

The given identity is 1/(1 + cosθ) + 1/(1 - cosθ) = 2cosec²θ

L.H.S.

Take LCM of denominators

⇒ 2/(1 + cosθ) × (1 - cosθ)

⇒ 2/(1 - cos²θ)

⇒ 2/sin²θ

⇒ 2 cosec²θ = R.H.S.

So, statement 1 is correct

Now, the given identity is (1 + tan²θ)/ cosec²θ = tan²θ

L.H.S.

⇒ (1 + tan²θ)/cosec²θ

⇒ sec²θ/cosec²θ

⇒ sin²θ/cos²θ

⇒ tan²θ = R.H.S.

So, statement 2 is correct

Hence, option (3) is correct