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If $sin θ = 2425,$ then which of the following is the value of the expression $sin 2 θ + cos 2 θ$ ?

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answer is A.

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Detailed Solution

The given trigonometric ratio is,

sin θ = 2425

We know that,

sin θ = P H

⇒ P H = 2425 = k (say) ⇒ P = 24 k, H = 25 k

Using Pythagoras theorem, we have,

H 2 = P 2 + B 2 ⇒ B 2 = 25 k 2 − 24 k 2 ⇒ B 2 = 49 k 2 ⇒ B = 7 k

We know the trigonometric ratio,

cos θ = B H ⇒ cos θ = 7 k 25 k = 725

Therefore we have,

sin 2 θ + cos 2 θ = 24252 + 7252 ⇒ 576 + 49 625 ⇒ 625625 = 1

Therefore, the value of the trigonometric expression

sin 2 θ + cos 2 θ = 1.

Hence, option (1) is correct.

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