જો sin theta = sin 15^{circ} + sin 45^{circ}, | vedclass

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(A) આપેલ છે $\sin 	heta = \sin 15^{\circ} + \sin 45^{\circ}$.સૂત્ર $\sin C + \sin D = 2 \sin \left( \frac{C+D}{2} ight) \cos \left( \frac{C-D}{2} \

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$75$

Vedclass · Answer

(A) આપેલ છે $\sin 	heta = \sin 15^{\circ} + \sin 45^{\circ}$.સૂત્ર $\sin C + \sin D = 2 \sin \left( \frac{C+D}{2} ight) \cos \left( \frac{C-D}{2} ight)$ નો ઉપયોગ કરતા:$\sin 	heta = 2 \sin \left( \frac{15^{\circ} + 45^{\circ}}{2} ight) \cos \left( \frac{15^{\circ} - 45^{\circ}}{2} ight)$$\sin 	heta = 2 \sin 30^{\circ} \cos(-15^{\circ})$$\cos(-x) = \cos x$ અને $\sin 30^{\circ} = \frac{1}{2}$ હોવાથી:$\sin 	heta = 2 	imes \frac{1}{2} 	imes \cos 15^{\circ}$$\sin 	heta = \cos 15^{\circ}$$\cos 15^{\circ} = \sin(90^{\circ} - 15^{\circ}) = \sin 75^{\circ}$ હોવાથી:$\sin 	heta = \sin 75^{\circ}$તેથી,$	heta = 75^{\circ}$.

જો $\sin \theta = \sin 15^{\circ} + \sin 45^{\circ}$,જ્યાં $0^{\circ} < \theta < 180^{\circ}$ હોય,તો $\theta =$ ($^{\circ}$ માં)

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