Mathematics
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?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Trigonometrical Ratios
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Answer
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.
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