Question:medium
If \( \tan A \) and \( \tan B \) are roots of the equation \( x^2 - 2x - 5 = 0 \), then the value of \( 10\left(\sin^2\left(\frac{A+B}{2}\right)\right) \) is:
If \( \tan A \) and \( \tan B \) are roots of the equation \( x^2 - 2x - 5 = 0 \), then the value of \( 10\left(\sin^2\left(\frac{A+B}{2}\right)\right) \) is:
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The expression \( 1 - \cos \theta \) is the standard bridge between trigonometric functions of a full angle and the squared sine of its half-angle.
Updated On: Apr 6, 2026
- \( 5 + \frac{3}{2}\sqrt{10} \)
- \( 10 + \frac{3}{2}\sqrt{10} \)
- \( 5 - \frac{3}{2}\sqrt{10} \)
- \( 10 - \frac{3}{2}\sqrt{10} \)
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The Correct Option is C
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