Consider the following two statements.

Statement 1: sin 18° - cos 72° = 0.

Statement 2: sin θ = cos (90° - θ).

Which of the following is valid?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.

Given,

sin 18° - cos 72° = 0

Solving L.H.S.,

⇒ sin (90° - 72°) - cos 72°

⇒ cos 72° - cos 72°

⇒ 0.

Since, L.H.S. = R.H.S. = 0.

∴ Statement 1 is true.

The statement sin θ = cos (90° - θ) is true.

This is a fundamental trigonometric identity, often referred to as the cofunction identity.

∴ Statement 2 is true.

∴ Both the statements are true.

Hence, option 1 is correct option.