If cos theta - 4 sin theta = 1,then sin theta | vedclass

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(D) Let $\cos 	heta - 4 \sin 	heta = 1$  $(i)$ and $\sin 	heta + 4 \cos 	heta = x$  $(ii)$.Squaring and adding both equations:$(\cos 	heta - 4 \s

Vedclass · Accepted Answer

$\pm 4$

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(D) Let $\cos 	heta - 4 \sin 	heta = 1$  $(i)$ and $\sin 	heta + 4 \cos 	heta = x$  $(ii)$.Squaring and adding both equations:$(\cos 	heta - 4 \sin 	heta)^2 + (\sin 	heta + 4 \cos 	heta)^2 = 1^2 + x^2$$(\cos^2 	heta + 16 \sin^2 	heta - 8 \sin 	heta \cos 	heta) + (\sin^2 	heta + 16 \cos^2 	heta + 8 \sin 	heta \cos 	heta) = 1 + x^2$$(\cos^2 	heta + \sin^2 	heta) + 16(\sin^2 	heta + \cos^2 	heta) = 1 + x^2$$1 + 16(1) = 1 + x^2$$17 = 1 + x^2$$x^2 = 16$$x = \pm 4$Thus,$\sin 	heta + 4 \cos 	heta = \pm 4$.

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

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