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Ex 3.4, 2 - sec x = 2, find principal and general solutions - Finding general solutions

  1. Chapter 3 Class 11th Trigonometric Functions
  2. Serial order wise
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Ex 3.4, 2 Find the principal and general solutions of the equation sec x = 2 Given sec x = 2 1/cos⁑π‘₯ = 2 1/2 = cos x cos x = 1/2 We know that cos 60Β° = 1/2 We find value of x where cos is positive cos is positive in Ist and lVth Quadrant Value in Ist Quadrant = 60Β° Value in lVth Quadrant = 360Β° – 60Β° = 300Β° So Principal solution are x = 60Β° and x = 300Β° x = 60 Γ— πœ‹/180 and x = 300 Γ— πœ‹/180 x = πœ‹/3 and x = 5πœ‹/3 To find general solution Let cos x = cos y and given cos x = 1/2 From (1) and (2) cos y = 1/2 cos y = cos πœ‹/3 β‡’ y = πœ‹/3 Since cos x = cos y General Solution is x = 2nΟ€ Β± y where n ∈ Z Put y = πœ‹/3 Hence, x = 2nΟ€ Β± πœ‹/3 where n ∈ Z

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