Question

If sin5theta=cos4theta where 5theta and 4theta are acute angles .Find the value of theta

Answer 1

Answer :

Now, sin5θ = cos4θ

⇒ cos (90 - 5θ) = cos4θ,
since sinθ = cos (90 - θ)

⇒ 90 - 5θ = 4θ

⇒ 4θ + 5θ = 90

⇒ 9θ = 90

⇒ θ = 90/9

⇒ θ = 10

We see that, 5θ = 50° and 4θ = 40°; both are acute angles.

Therefore, the value of θ is 10°

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Answer 2

Sin5Ф = Cos4Ф

⇒ Cos(90 - 5Ф) = Cos4Ф  [cos(90-Ф)= sinФ]

⇒  90 - 5Ф = 4Ф

⇒  90 = 4Ф + 5Ф

⇒ 90 = 9Ф

⇒ 90/9 = Ф

⇒  10 = Ф



Value of theta is 10°




i hope this will help you



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