જો cos x+cos y+cos alpha=0 અને sin x+sin y+si | vedclass

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Question

(D) આપેલ છે,$\cos x+\cos y=-\cos \alpha$  $(i)$ સૂત્ર $\cos C + \cos D = 2 \cos \left(\frac{C+D}{2}\right) \cos \left(\frac{C-D}{2}\right)$ નો ઉપયોગ ક

Vedclass · Accepted Answer

$\cot \alpha$

Vedclass · Answer

(D) આપેલ છે,$\cos x+\cos y=-\cos \alpha$  $(i)$ સૂત્ર $\cos C + \cos D = 2 \cos \left(\frac{C+D}{2}\right) \cos \left(\frac{C-D}{2}\right)$ નો ઉપયોગ કરતા: $2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right) = -\cos \alpha$ તેમજ,$\sin x+\sin y=-\sin \alpha$  (ii) સૂત્ર $\sin C + \sin D = 2 \sin \left(\frac{C+D}{2}\right) \cos \left(\frac{C-D}{2}\right)$ નો ઉપયોગ કરતા: $2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right) = -\sin \alpha$ સમીકરણ $(i)$ ને સમીકરણ (ii) વડે ભાગતા: $\frac{2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)}{2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)} = \frac{-\cos \alpha}{-\sin \alpha}$ $\cot \left(\frac{x+y}{2}\right) = \cot \alpha$

જો $\cos x+\cos y+\cos \alpha=0$ અને $\sin x+\sin y+\sin \alpha=0$ હોય,તો $\cot \left(\frac{x+y}{2}\right)$ ની કિંમત શોધો.

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