Class 10 Exam > Class 10 Questions > If sin 5θ = cos 4θ, where 5&theta...
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If sin 5θ = cos 4θ, where 5θ and 4θ are acute angles, then the value of θ is
- a)15°
- b)8°
- c)10°
- d)12°
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If sin 5θ = cos 4θ, where 5θ and 4θ are acute ...
Given Information:
- sin 5θ = cos 4θ
- 5θ and 4θ are acute angles
Solution:
Step 1: Use Trigonometric Identities
- We know that sin(90° - θ) = cosθ
- Therefore, sin(90° - 5θ) = cos 5θ
- Similarly, sin(90° - 4θ) = cos 4θ
Step 2: Substitute the Values
- Given sin 5θ = cos 4θ
- This can be rewritten as sin(90° - 5θ) = sin(90° - 4θ)
Step 3: Equate the Angles
- Setting the angles equal to each other:
90° - 5θ = 90° - 4θ
- Simplifying the equation:
-5θ = -4θ
θ = 10°
Therefore, the value of θ is 10°.
- sin 5θ = cos 4θ
- 5θ and 4θ are acute angles
Solution:
Step 1: Use Trigonometric Identities
- We know that sin(90° - θ) = cosθ
- Therefore, sin(90° - 5θ) = cos 5θ
- Similarly, sin(90° - 4θ) = cos 4θ
Step 2: Substitute the Values
- Given sin 5θ = cos 4θ
- This can be rewritten as sin(90° - 5θ) = sin(90° - 4θ)
Step 3: Equate the Angles
- Setting the angles equal to each other:
90° - 5θ = 90° - 4θ
- Simplifying the equation:
-5θ = -4θ
θ = 10°
Therefore, the value of θ is 10°.
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Community Answer
If sin 5θ = cos 4θ, where 5θ and 4θ are acute ...
We have
sin 5θ = cos 4θ
⇒ cos (90° – 5θ) = cos 4θ
⇒ 90° – 5θ = 4θ
⇒ 4θ + 5θ = 90°
⇒ 9θ = 90°
⇒ θ = 10°
sin 5θ = cos 4θ
⇒ cos (90° – 5θ) = cos 4θ
⇒ 90° – 5θ = 4θ
⇒ 4θ + 5θ = 90°
⇒ 9θ = 90°
⇒ θ = 10°
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If sin 5θ = cos 4θ, where 5θ and 4θ are acute angles, then the value of θ isa)15°b)8°c)10°d)12°Correct answer is option 'C'. Can you explain this answer?
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