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AP EAMCET202120 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

If in ∆ A B C , a tan A + b tan B = ( a + b ) · tan A + B 2 , then which of the following holds?

Options

  1. AA = B
  2. BA = 2   B
  3. CA = 1 2 B
  4. DA > B

Correct answer

A. A = B

Step-by-step solution

Given that: a tan A + b tan B = ( a + b ) · tan A + B 2 ⇒ a tan A - tan A + B 2 = b tan A + B 2 - tan B ⇒ a sin A cos A - sin A + B 2 cos A + B 2 = b sin A + B 2 cos A + B 2 - sin B cos B ⇒ a sin A cos A + B 2 - cos A sin A + B 2 cos A cos A + B 2 = b cos B sin A + B 2 - sin B cos A + B 2 cos B cos A + B 2 ⇒ a sin A - A + B 2 cos A cos A + B 2 = b sin A + B 2 - B cos B cos A + B 2 ⇒ a sin A - B 2 cos A = b sin A - B 2 cos B ⇒ sin A - B 2 a cos A - b cos B = 0 As we know that

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