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CDS 2024 · PYQ · Trigonometry · medium

If t = cos 79°, then what is cosec 79° (1 − cos 79°) equal to ?

Answer

The correct answer is D: √((1−t)/(1+t)). cosec 79° (1 − cos 79°) = (1 − t)/sin 79° = (1 − t)/√(1 − t²) = (1 − t)/√((1−t)(1+t)) = √((1−t)/(1+t)).

  1. A.√((1+t)/(1−t))
  2. B.t/√(1−t²)
  3. C.√(1−t²)/t
  4. D.√((1−t)/(1+t))✓ Correct

Explanation

cosec 79° (1 − cos 79°) = (1 − t)/sin 79° = (1 − t)/√(1 − t²) = (1 − t)/√((1−t)(1+t)) = √((1−t)/(1+t)).
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