If 5 cos theta + 12 sin theta = 13 and 0^{cir | vedclass

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Question

(A) Given equation: $5 \cos 	heta + 12 \sin 	heta = 13$.Divide both sides by $13$:$\frac{5}{13} \cos 	heta + \frac{12}{13} \sin 	heta = 1$.We know

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$\frac{12}{13}$

Vedclass · Answer

(A) Given equation: $5 \cos 	heta + 12 \sin 	heta = 13$.Divide both sides by $13$:$\frac{5}{13} \cos 	heta + \frac{12}{13} \sin 	heta = 1$.We know the identity $\sin^2 	heta + \cos^2 	heta = 1$. Comparing this with the standard form $\cos \alpha \cos 	heta + \sin \alpha \sin 	heta = \cos(	heta - \alpha) = 1$,we can set $\cos \alpha = \frac{5}{13}$ and $\sin \alpha = \frac{12}{13}$.Then $\cos \alpha \cos 	heta + \sin \alpha \sin 	heta = 1 \implies \cos(	heta - \alpha) = 1$.Since $0^{\circ} Therefore,$\sin 	heta = \sin \alpha = \frac{12}{13}$.

If $5 \cos \theta + 12 \sin \theta = 13$ and $0^{\circ} < \theta < 90^{\circ}$,then the value of $\sin \theta$ is:

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