The value of frac{sin 150^{circ}-5 cos 300^{c | vedclass

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(D) Given expression: $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 	an 225^{\circ}}{	an 135^{\circ}+3 \sin 210^{\circ}}$Using trigonometric reductio

Vedclass · Accepted Answer

$-2$

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(D) Given expression: $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 	an 225^{\circ}}{	an 135^{\circ}+3 \sin 210^{\circ}}$Using trigonometric reduction formulas:$\sin 150^{\circ} = \sin(180^{\circ}-30^{\circ}) = \sin 30^{\circ} = \frac{1}{2}$$\cos 300^{\circ} = \cos(360^{\circ}-60^{\circ}) = \cos 60^{\circ} = \frac{1}{2}$$	an 225^{\circ} = 	an(180^{\circ}+45^{\circ}) = 	an 45^{\circ} = 1$$	an 135^{\circ} = 	an(180^{\circ}-45^{\circ}) = -	an 45^{\circ} = -1$$\sin 210^{\circ} = \sin(180^{\circ}+30^{\circ}) = -\sin 30^{\circ} = -\frac{1}{2}$Substituting these values into the expression:$= \frac{\frac{1}{2} - 5(\frac{1}{2}) + 7(1)}{-1 + 3(-\frac{1}{2})}$$= \frac{\frac{1}{2} - \frac{5}{2} + 7}{-1 - \frac{3}{2}}$$= \frac{-2 + 7}{-\frac{5}{2}} = \frac{5}{-\frac{5}{2}} = -2$

The value of $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 \tan 225^{\circ}}{\tan 135^{\circ}+3 \sin 210^{\circ}}$ is

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