sin 105^{circ} + cos 105^{circ} का मान क्या ह | vedclass

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(A) हम जानते हैं कि $\sin 105^{\circ} = \sin(60^{\circ} + 45^{\circ}) = \sin 60^{\circ} \cos 45^{\circ} + \cos 60^{\circ} \sin 45^{\circ} = \frac{\sqr

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

Vedclass · Answer

(A) हम जानते हैं कि $\sin 105^{\circ} = \sin(60^{\circ} + 45^{\circ}) = \sin 60^{\circ} \cos 45^{\circ} + \cos 60^{\circ} \sin 45^{\circ} = \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} + \frac{1}{2} \cdot \frac{1}{\sqrt{2}} = \frac{\sqrt{3} + 1}{2\sqrt{2}}$.साथ ही,$\cos 105^{\circ} = \cos(60^{\circ} + 45^{\circ}) = \cos 60^{\circ} \cos 45^{\circ} - \sin 60^{\circ} \sin 45^{\circ} = \frac{1}{2} \cdot \frac{1}{\sqrt{2}} - \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}} = \frac{1 - \sqrt{3}}{2\sqrt{2}}$.इन दोनों मानों को जोड़ने पर:$\sin 105^{\circ} + \cos 105^{\circ} = \frac{\sqrt{3} + 1}{2\sqrt{2}} + \frac{1 - \sqrt{3}}{2\sqrt{2}} = \frac{\sqrt{3} + 1 + 1 - \sqrt{3}}{2\sqrt{2}} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}}$.

$\sin 105^{\circ} + \cos 105^{\circ}$ का मान क्या है?

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