Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202615 April 2026Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In ABC , with the usual notations, C = 90^ , then (A - B) is equal to....

Options

  1. Aa^2 + b^2 a^2 - b^2
  2. Ba^2 + c^2 a^2 - c^2
  3. Cb^2 + c^2 b^2 - c^2
  4. Da^2 - b^2 a^2 + b^2

Correct answer

D. a^2 - b^2 a^2 + b^2

Step-by-step solution

In ABC , C = 90^ . Using trigonometric ratios in a right-angled triangle: A = a c A = b c B = b c B = a c Using the expansion formula for (A - B) : (A - B) = A B - A B Substituting the values: (A - B) = ( a c ) ( a c ) - ( b c ) ( b c ) (A - B) = a^2 - b^2 c^2 By Pythagoras theorem in ABC , c^2 = a^2 + b^2 . Substituting c^2 = a^2 + b^2 : (A - B) = a^2 - b^2 a^2 + b^2 Answer: a^2 - b^2 a^2 + b^2

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If x+ x= 1 2 and 0 < x < , then x= 2025If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B= 2025In a ABC , if ^2 ~B = A and 2 ^2 ~A =3 ^2 ~B , then the triangle is 202512 2 12 3 12 4 12 5 12 6 12 = 2025If ( 4 + )= ^3 ( 4 + ) , then ( + ) ( - )= 2025If A+B+C+D=2 , then A+ B+ C+ D= 2025(4 ^2 20 -1 ) (4 ^2 3 20 -1 ) (4 ^2 5 20 +1 ) (4 ^2 7 20 -1 ) (4 ^2 9 20 -1 )= 2025If A and B are the values such that (A+B) and (A-B) are not odd multiples of 2 and 2 (A+B)=3 (A-B) , then A A= 2025 Full Trigonometric Ratios & Identities list All MHT CET PYQs