left(frac{sin 35^{circ}}{cos 55^{circ}}right) | vedclass

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Question

(B) Given expression: $\left(\frac{\sin 35^{\circ}}{\cos 55^{\circ}}\right)^2+\left(\frac{\cos 55^{\circ}}{\sin 35^{\circ}}\right)^2-2 \cos 30^{\circ}

Vedclass · Accepted Answer

$2-\sqrt{3}$

Vedclass · Answer

(B) Given expression: $\left(\frac{\sin 35^{\circ}}{\cos 55^{\circ}}\right)^2+\left(\frac{\cos 55^{\circ}}{\sin 35^{\circ}}\right)^2-2 \cos 30^{\circ}$ Since $\cos 55^{\circ} = \cos(90^{\circ}-35^{\circ}) = \sin 35^{\circ}$,we substitute this into the expression: $= \left(\frac{\sin 35^{\circ}}{\sin 35^{\circ}}\right)^2 + \left(\frac{\sin 35^{\circ}}{\sin 35^{\circ}}\right)^2 - 2 \cos 30^{\circ}$ $= (1)^2 + (1)^2 - 2 \left(\frac{\sqrt{3}}{2}\right)$ $= 1 + 1 - \sqrt{3}$ $= 2 - \sqrt{3}$

$\left(\frac{\sin 35^{\circ}}{\cos 55^{\circ}}\right)^2+\left(\frac{\cos 55^{\circ}}{\sin 35^{\circ}}\right)^2-2 \cos 30^{\circ}=$

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