\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 $\mathbf{\frac{22}{\lambda}=}$
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2 Answers
36divide both sides by 2√2
√3 - 12√2 sin x + √3 + 12√2 cos x = 2
=> sin15° cosx + cos15° sinx = 2 sinx.cosx
=> sin (15° + x) = sin 2x
=> sin 2x - sin (15° + x) = 0
=> 2 sin (x - 15°2) . sin (3x +15°2) = 0
other soln. then 15° is
3x +15°2 = 90
=> x = 165/3 = 55°
now, ∩/36 = 5 therefore, λ = 11 => 22/λ = 2 Ans.!!
