यदि |k|, = 5 तथा {0^o} le theta le {360 | vedclass

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Question

$3\cos 	heta  + 4\sin 	heta  = 5\,\left[ {\frac{3}{5}\cos 	heta  + \frac{4}{5}\sin 	heta } ight] = 5\cos (	heta  - \alpha )

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दो

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$3\cos 	heta  + 4\sin 	heta  = 5\,\left[ {\frac{3}{5}\cos 	heta  + \frac{4}{5}\sin 	heta } ight] = 5\cos (	heta  - \alpha )$

जहाँ $\cos \alpha  = \frac{3}{5}$, $\sin \alpha  = \frac{4}{5}$.

अब $3\cos 	heta  + 4\sin 	heta  = k$

$	herefore$ $5\cos (	heta  - \alpha ) = k $

$\Rightarrow \cos (	heta  - \alpha ) =  \pm 1$

$ \Rightarrow $ $	heta  - \alpha  = {0^o},\,{180^o} $

$\Rightarrow 	heta  = \alpha ,\,{m{ }}{180^o} + \alpha $.

यदि $|k|\, = 5$ तथा ${0^o} \le \theta \le {360^o}$, तब 3$\cos \theta + 4\sin \theta = k$ के विभिन्न हलों की संख्या होंगी

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