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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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In triangle ABC, the value of cot⁡A2cot⁡B2−1cot⁡A2cot⁡B2\frac{{\cot \frac{A}{2}\cot \frac{B}{2} - 1}}{{\cot \frac{A}{2}\cot \frac{B}{2}}} is
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Correct option: D
2ca+b+c\frac{{2c}}{{a + b + c}}
Option D (2ca+b+c\frac{{2c}}{{a + b + c}}) is correct because simplifying the given expression using trigonometric identities and half-angle formulas leads to the result cs\frac{c}{s}, where ss is the semi-perimeter of the triangle, which is equal to 2ca+b+c\frac{{2c}}{{a + b + c}}.

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