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MHT CET202521 Apr 2025Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of 20^ 80^ 50^ =

Options

  1. A3
  2. B1 3
  3. C1 2 3
  4. D2 3

Correct answer

A. 3

Step-by-step solution

Evaluate the expression 20^ 80^ 50^ . Note that 50^ = 40^ , converting via the complementary identity. Substituting gives 20^ 80^ 40^ . Rearranged, this is 20^ 40^ 80^ . This matches the identity (60^ - ) (60^ + ) = 3 with = 20^ , since 60^ - 20^ = 40^ and 60^ + 20^ = 80^ . Thus, 20^ 40^ 80^ = 60^ = 3 . The value is 3 , so option A is correct.

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