The value of cos 255^o + sin 195^o is | vedclass

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(C) Given expression: $\cos 255^o + \sin 195^o$We can write the angles as:$\cos 255^o = \cos(270^o - 15^o) = -\sin 15^o$$\sin 195^o = \sin(180^o + 15^

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$-\frac{\sqrt{3} - 1}{\sqrt{2}}$

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(C) Given expression: $\cos 255^o + \sin 195^o$We can write the angles as:$\cos 255^o = \cos(270^o - 15^o) = -\sin 15^o$$\sin 195^o = \sin(180^o + 15^o) = -\sin 15^o$Substituting these values:$-\sin 15^o - \sin 15^o = -2 \sin 15^o$We know that $\sin 15^o = \sin(45^o - 30^o) = \sin 45^o \cos 30^o - \cos 45^o \sin 30^o = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} \cdot \frac{1}{2} = \frac{\sqrt{3} - 1}{2\sqrt{2}}$Therefore,$-2 \sin 15^o = -2 \left( \frac{\sqrt{3} - 1}{2\sqrt{2}} \right) = -\frac{\sqrt{3} - 1}{\sqrt{2}}$

The value of $\cos 255^o + \sin 195^o$ is

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