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MHT CET2016MathematicsProperties of Triangles

In A B C ( a − b ) 2 cos 2 C 2 + ( a + b ) 2 sin 2 C 2 =

Options

  1. Ab 2
  2. Bc 2
  3. Ca 2
  4. Da 2 + b 2 + c 2

Correct answer

B. c 2

Step-by-step solution

Let X = a - b 2 cos 2 ⁡ C 2 + a + b 2 sin 2 ⁡ C 2 = ( a 2 + b 2 ) ( cos 2 ⁡ C 2 + sin 2 ⁡ C 2 ) - 2 a b ( cos 2 ⁡ C 2 - sin 2 ⁡ C 2 ) = a 2 + b 2 - 2 a b cos ⁡ C = c 2 ∵ ( c o s i n e rule )

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