\(\rm \frac{cosA+cosB}{sinA-sinB}=\)

  1. \(\rm tan\frac{A+B}{2}\)
  2. \(\rm tan\frac{A-B}{2}\)
  3. \(\rm cot\frac{A+B}{2}\)
  4. \(\rm cot\frac{A-B}{2}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm cot\frac{A-B}{2}\)
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Detailed Solution

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अवधारण:

\(\rm sinA - sin B = 2cos\frac{A+B}{2}sin\frac{A-B}{2}\)

\(\rm cosA+cosB=2cos\frac{A+B}{2}cos\frac{A-B}{2}\)

 

गणना:

\(\rm \frac{cosA+cosB}{sinA-sinB}=\)

\(\rm \frac {2cos\frac{A+B}{2}cos\frac{A-B}{2}}{2cos\frac{A+B}{2}sin\frac{A-B}{2}}\)

=\(\rm cot\frac{A-B}{2}\)

इसलिए, विकल्प (4) सही है।

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