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MHT CET202611 April 2026Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of ^2 10^ - 10^ 50^ + ^2 50^ is equal to....

Options

  1. A1 4
  2. B1 2
  3. C3 4
  4. D1

Correct answer

C. 3 4

Step-by-step solution

Given expression: ^2 10^ - 10^ 50^ + ^2 50^ Multiplying and dividing by 2 : = 1 2 [ 2 ^2 10^ - 2 10^ 50^ + 2 ^2 50^ ] Using the identities 2 ^2 = 1 + 2 and 2 A B = (A+B) + (A-B) : = 1 2 [ (1 + 20^ ) - ( 60^ + 40^ ) + (1 + 100^ ) ] Substituting 60^ = 1 2 : = 1 2 [ 1 + 20^ - 1 2 - 40^ + 1 + 100^ ] = 1 2 [ 3 2 + ( 100^ + 20^ ) - 40^ ] Applying the sum-to-product formula C + D = 2 ( C+D 2 ) ( C-D 2 ) : 100^ + 20^ = 2 60^ 40^ = 2 ( 1 2 ) 40^ = 40^ Substituting this back into the expression: = 1 2 [ 3 2 + 40^ - 40^ ] = 1

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