Question:
A line makes angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma \) is equal to
A line makes angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma \) is equal to
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Remember the identity for angles in a line: \( \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \), which helps in solving problems with angles and trigonometric functions.
Updated On: Jan 27, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Use the property of the angles.
For a line making angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, we use the identity: \[ \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \]
Step 2: Calculate the sum.
Using the identity, we have: \[ \cos 2\alpha + \cos 2\beta + \cos 2\gamma = -1 \]
Step 3: Conclusion.
The correct answer is \( -1 \).
For a line making angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, we use the identity: \[ \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \]
Step 2: Calculate the sum.
Using the identity, we have: \[ \cos 2\alpha + \cos 2\beta + \cos 2\gamma = -1 \]
Step 3: Conclusion.
The correct answer is \( -1 \).
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