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solve the equation cos x + sin x (frac{1}{cos x – sinx}) for values of…

solve the equation cos x + sin x (frac{1}{cos x – sinx}) for values of such that 0 (leq) x

  • A.
    (frac{pi}{2}), (frac{3pi}{2})
  • B.
    (frac{pi}{3}), (frac{2pi}{3})
  • C.
    0, (frac{pi}{3})
  • D.
    0, (pi)
Correct Answer: Option D
Explanation

cos x + sin x (frac{1}{cos x – sinx})
= (cosx + sinx)(cosx – sinx) = 1
= cos2x + sin2x = 1
cos2x – (1 – cos2x) = 1
= 2cos2x = 2
cos2x = 1
= cosx = (pm)1 = x
= cos-1x ((pm), 1)
= 0, (pi) (frac{3}{2}pi), 2(pi)
(possible solution)