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If 4 cos2 A + 2 sin2 A = 3, then what is the value of A, given that A lies in the first quadrant?
- a)45°
- b)60°
- c)30°
- d)15°
Correct answer is option 'A'. Can you explain this answer?
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If 4 cos2 A + 2 sin2 A = 3, then what is the value of A, given that A ...
To find the value of A, we can start by using the identity cos2A + sin2A = 1. By rearranging the given equation, we have:
4 cos2A - 2(1 - cos2A) = 3
4 cos2A - 2 + 2 cos2A = 3
6 cos2A = 5
cos2A = 5/6
Since A lies in the first quadrant, cos A is positive. Taking the square root of both sides, we have:
cos A = √(5/6)
To find the value of A, we can use the inverse cosine function:
A = cos^(-1)(√(5/6))
Using a calculator, we find:
A ≈ 0.7227 radians ≈ 41.41 degrees
Therefore, the value of A is approximately 41.41 degrees.
4 cos2A - 2(1 - cos2A) = 3
4 cos2A - 2 + 2 cos2A = 3
6 cos2A = 5
cos2A = 5/6
Since A lies in the first quadrant, cos A is positive. Taking the square root of both sides, we have:
cos A = √(5/6)
To find the value of A, we can use the inverse cosine function:
A = cos^(-1)(√(5/6))
Using a calculator, we find:
A ≈ 0.7227 radians ≈ 41.41 degrees
Therefore, the value of A is approximately 41.41 degrees.
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If 4 cos2 A + 2 sin2 A = 3, then what is the value of A, given that A lies in the first quadrant?a)45°b)60°c)30°d)15°Correct answer is option 'A'. Can you explain this answer?
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