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MHT CET202520 Apr 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

With usual notations, in a triangle ABC , if is any real number, then a (B- )+b (A+ ) is

Options

  1. Aa
  2. Bb
  3. Cc

Correct answer

3

Step-by-step solution

The expression E = a (B - ) + b (A + ) is given, where a , b , A , and B are triangle elements. By the sine rule, let a = k A and b = k B for some constant k . Substituting yields E = k A (B - ) + k B (A + ) . Expanding using cosine sum and difference identities gives E = k [ A ( B + B ) + B ( A - A )] . Simplifying further, the A B terms cancel, leaving E = k [ A B + B A ] . Factoring results in E = k ( A B + A B) . Applying the sine addition formula, A B + A B = (A + B) . Since A + B + C = in a triangle, (A + B)

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