Trigonometric equation.

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\hspace{-16}$In $\mathbf{\left(0,\frac{\pi}{2}\right)},$ one Solution of $\mathbf{\frac{\sqrt{3}-1}{\sin x}+\frac{\sqrt{3}+1}{\cos x}=4\sqrt{2}}$\\\\\\ is $\frac{\pi}{12}$ and other solution is $\mathbf{\frac{\lambda.\pi}{36}}$. Then $\mathbf{\frac{22}{\lambda}=}$

#Mathematics #Trignometry

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2 Answers

36

rahul ·2012-03-11 22:24:20

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36

rahul ·2012-03-11 22:31:37

divide both sides by 2âˆš2

âˆš3 - 12âˆš2 sin x + âˆš3 + 12âˆš2 cos x = 2

=> sin15Â° cosx + cos15Â° sinx = 2 sinx.cosx

=> sin (15Â° + x) = sin 2x

=> sin 2x - sin (15Â° + x) = 0

=> 2 sin (x - 15Â°2) . sin (3x +15Â°2) = 0

other soln. then 15Â° is
3x +15Â°2 = 90

=> x = 165/3 = 55Â°

now, âˆ©/36 = 5 therefore, Î» = 11 => 22/Î» = 2 Ans.!!

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