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COMEDK202510 May 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of 1 2 10^ -2 70^ is

Options

  1. A- 3 2
  2. B0
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

Let E = 1 2 10^ - 2 70^ . Expressing the expression with a common denominator: E = 1 - 4 10^ 70^ 2 10^ Using the product-to-sum formula 2 A B = (A - B) - (A + B) : 4 10^ 70^ = 2 [2 70^ 10^ ] = 2 [ (70^ - 10^ ) - (70^ + 10^ )] = 2 [ 60^ - 80^ ] = 2 [ 1 2 - 80^ ] = 1 - 2 80^ Substituting this back into the expression for E : E = 1 - (1 - 2 80^ ) 2 10^ = 2 80^ 2 10^ Since 80^ = (90^ - 80^ ) = 10^ : E = 10^ 10^ = 1 Answer: 1

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