√(3)sinθ cosθ= √(2) ⇒√(3)2sinθ 12cosθ= 1√(2) ⇒sin(θ π3)= sinπ4 ⇒θ π3= n π+( 1)^n π/4 ⇒θ= n π+π3+( 1)^n π/4 ...

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Use of Trigonometric Table

√3sinθ -cosθ ...

Question

$\sqrt{3} sin θ - cos θ = \sqrt{2}$ .

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Solution

$\sqrt{3} sin θ - cos θ = \sqrt{2}$
$\Rightarrow \frac{\sqrt{3}}{2} sin θ - \frac{1}{2} cos θ = \frac{1}{\sqrt{2}}$
$\Rightarrow sin (θ - \frac{π}{3}) = sin \frac{π}{4}$
$\Rightarrow θ - \frac{π}{3} = n π + (- 1)^{n} π / 4$
$\Rightarrow θ = n π + \frac{π}{3} + (- 1)^{n} π / 4$

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