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KCET2011MathematicsTrigonometric Ratios & Identities

The value of 10^ 30^ 50^ 70^ is

Options

  1. A1 8
  2. B3 16
  3. C3 16
  4. D1 16

Correct answer

D. 1 16

Step-by-step solution

aligned 10^ & 30^ 50^ 70^ &= 1 2 10^ 1 2 (2 70^ 50^ ) &= 1 2 10^ 1 2 (70^ -50^ ) . &= 1 2 10^ 1 2 (70^ +50^ ) &= 1 2 10^ 1 2 ( 10^ + 1 2 ) &= 1 4 10^ 20^ + 1 8 10^ &= 1 4 1 2 ( 30^ - 10^ )+ 1 8 10^ &= 1 8 30^ - 1 8 10^ +1 / 8 10^ &= 1 8 1 2 -0= 1 16 aligned

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