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The value of 3 cosec 20^ - 20^ 20^ 40^ 60^ 80^ is equal to

Options

  1. A16
  2. B32
  3. C64
  4. D12

Correct answer

C. 64

Step-by-step solution

Numerator: 3 cosec 20° - 20° = 3 20° - 20° 20° 20° 3 20° - 20° = 2 ( 3 2 20° - 1 2 20° ) = 2 (20° + 30°) = 2 50° So numerator = 2 50° 20° 20° = 4 50° 40° = 4 Denominator: 20° 40° 60° 80° where 60° = 1 2 Using product formula: 20° 20° 40° 80° = 1 8 20° Therefore 20° 40° 80° 1 2 = 1 16 So, 4 20° 20° 1 16 = 64

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