જો sin 3alpha = 4sin alpha sin (x + alpha )si | vedclass

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Question

(B) આપેલ સમીકરણ: $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha )$નિત્યસમ $\sin (x + \alpha )\sin (x - \alpha ) = \sin^2 x - \sin^2 \

Vedclass · Accepted Answer

$n\pi \pm \frac{\pi }{3}$

Vedclass · Answer

(B) આપેલ સમીકરણ: $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha )$નિત્યસમ $\sin (x + \alpha )\sin (x - \alpha ) = \sin^2 x - \sin^2 \alpha$ નો ઉપયોગ કરતા:$\sin 3\alpha = 4\sin \alpha (\sin^2 x - \sin^2 \alpha)$નિત્યસમ $\sin 3\alpha = 3\sin \alpha - 4\sin^3 \alpha$ નો ઉપયોગ કરતા:$3\sin \alpha - 4\sin^3 \alpha = 4\sin \alpha \sin^2 x - 4\sin^3 \alpha$$3\sin \alpha = 4\sin \alpha \sin^2 x$$\sin \alpha 
eq 0$ ધારીને,$\sin \alpha$ વડે ભાગતા:$3 = 4\sin^2 x$$\sin^2 x = \frac{3}{4} = \left(\frac{\sqrt{3}}{2}ight)^2$$\sin^2 x = \sin^2 \left(\frac{\pi}{3}ight)$$\sin^2 x = \sin^2 	heta$ માટે વ્યાપક ઉકેલ $x = n\pi \pm 	heta$ છે.તેથી,$x = n\pi \pm \frac{\pi}{3}$.

જો $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ હોય,તો $x = $

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