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  4. The value of the expression (1/√3 sin (250°))+(1/ cos (290°)) is

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Q. The value of the expression $\frac{1}{\sqrt{3} \sin \left(250^{\circ}\right)}+\frac{1}{\cos \left(290^{\circ}\right)}$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$E=\frac{1}{\sin 20^{\circ}}-\frac{1}{\sqrt{3} \cos 20^{\circ}}=\frac{\frac{\sqrt{3}}{2} \cos 20^{\circ}-\frac{1}{2} \sin 20^{\circ}}{\frac{\sqrt{3}}{2} \sin 20^{\circ} \cos 20^{\circ}}=\frac{\sin \left(60^{\circ}-20^{\circ}\right)}{\frac{\sqrt{3}}{4} \cdot \sin 40^{\circ}}$