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MHT CET202611 April 2026Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In ABC , if A = 90^ , then (B - C) =

Options

  1. Aa^2 - c^2 a^2 + c^2
  2. Bc^2 - a^2 c^2 + a^2
  3. Cb^2 - c^2 b^2 + c^2
  4. Dc^2 - b^2 c^2 + b^2

Correct answer

C. b^2 - c^2 b^2 + c^2

Step-by-step solution

Given A = 90^ , ABC is a right-angled triangle with hypotenuse a . From the properties of a right-angled triangle, B = b a , B = c a , C = c a , and C = b a . Using the expansion formula for sine: (B - C) = B C - B C Substituting the trigonometric ratios: (B - C) = ( b a ) ( b a ) - ( c a ) ( c a ) (B - C) = b^2 - c^2 a^2 Using Pythagoras theorem, a^2 = b^2 + c^2 . Therefore, (B - C) = b^2 - c^2 b^2 + c^2 .

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