sin 2A = 2 sinA is true when A =
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We are given the equation:
sin 2A = 2 sin A.
Step 1: Recall the double-angle identity for sine
The double-angle identity for sine is:
sin 2A = 2 sin A cos A.
Substitute this into the given equation:
2 sin A cos A = 2 sin A.
Step 2: Simplify the equation
Divide both sides of the equation by 2 (assuming sin A ≠ 0):
sin A cos A = sin A.
Rearrange the terms:
sin A cos A – sin A = 0.
Factor out sin A:
sin A (cos A – 1) = 0.
Step 3: Solve for A
This equation is satisfied if either:
1. sin A = 0, or
2. cos A – 1 = 0.
Case 1: sin A = 0
The sine function is zero when A = 0°, 180°, etc. Among the given options, A = 0° satisfies this condition.
Case 2: cos A – 1 = 0
Solve for cos A:
cos A = 1.
The cosine function equals 1 when A = 0°, 360°, etc. Again, among the given options, A = 0° satisfies this condition.
Step 4: Verify the solution
Substitute A = 0° into the original equation:
sin 2(0°) = 2 sin(0°).
The left-hand side:
sin 2(0°) = sin 0° = 0.
The right-hand side:
2 sin(0°) = 2(0) = 0.
Since both sides are equal, A = 0° satisfies the equation.
Step 5: Final Answer
The value of A is 0°.
The correct answer is:
a) 0°
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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