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find the general solution of the equation (√3 -1)cosθ + (√3 +1)sinθ=2

find the general solution of the equation (√3 -1)cosθ + (√3 +1)sinθ=2

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
Simplifying:2 sqrt(2) sin(theta + pi/12) = 2
Divide both sides by 2 sqrt(2):
sin(theta + pi/12) = 1/sqrt(2)
Taking inverse sine of both sides:
theta + pi/12 = 2 pi n + (3 pi)/4  for  n  belongs to Z
   or  theta + pi/12 = 2 pi n + pi/4  for  n  belongs to Z
Subtracting pi/12 from both sides:
theta = 2 pi n + (2 pi)/3  for  n  belongs to Z
   or  theta + pi/12 = 2 pi n + pi/4  for  n  belongs to Z
Subtracting  pi/12 from both sides we get answer as-
theta = 2 pi n + (2 pi)/3  for  n  belongs to Z
   or  theta = 2 pi n + pi/6  for  n  belongs to Z.
 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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