The value of cos 105^circ + sin 105^circ is: | vedclass

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(D) We are given the expression $\cos 105^\circ + \sin 105^\circ$.Using the trigonometric identities $\cos(90^\circ + 	heta) = -\sin 	heta$ and $\si

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) We are given the expression $\cos 105^\circ + \sin 105^\circ$.Using the trigonometric identities $\cos(90^\circ + 	heta) = -\sin 	heta$ and $\sin(90^\circ + 	heta) = \cos 	heta$:$\cos 105^\circ = \cos(90^\circ + 15^\circ) = -\sin 15^\circ$$\sin 105^\circ = \sin(90^\circ + 15^\circ) = \cos 15^\circ$Substituting these values into the expression:$\cos 105^\circ + \sin 105^\circ = \cos 15^\circ - \sin 15^\circ$Using the values $\cos 15^\circ = \frac{\sqrt{3} + 1}{2\sqrt{2}}$ and $\sin 15^\circ = \frac{\sqrt{3} - 1}{2\sqrt{2}}$:$= \frac{\sqrt{3} + 1}{2\sqrt{2}} - \frac{\sqrt{3} - 1}{2\sqrt{2}}$$= \frac{\sqrt{3} + 1 - \sqrt{3} + 1}{2\sqrt{2}}$$= \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}}$.

The value of $\cos 105^\circ + \sin 105^\circ$ is:

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