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MHT CET202520 Apr 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of 3 20^ -4 20^ is equal to

Options

  1. A1
  2. B-1
  3. C0
  4. D1 2

Correct answer

A. 1

Step-by-step solution

Let E = 3 20^ - 4 20^ . Rewriting using trigonometric identities: E = 3 20^ 20^ - 4 20^ = 3 20^ - 4 20^ 20^ 20^ . Applying the double-angle identity 2 A A = 2A , we have 4 20^ 20^ = 2 40^ , so E = 3 20^ - 2 40^ 20^ . Using angle subtraction for sine: 40^ = (60^ - 20^ ) = 60^ 20^ - 60^ 20^ = 3 2 20^ - 1 2 20^ . Substituting back: E = 3 20^ - 2 ( 3 2 20^ - 1 2 20^ ) 20^ = 3 20^ - 3 20^ + 20^ 20^ = 20^ 20^ = 1 . Final answer: E = 1 , corresponding to option A.

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