Question

sin theta/1-cot theta+cos theta/1-than theta is equal to a.0 b.1 c. sin theta+cos theta d.sin theta-cos theta​

Answer 1

Answer:

$\frac{ \sin(a) }{1 - \cot(a) } + \frac{ \cos(a) }{1 - \tan(a) } \\ = \frac{ \sin {}^{2} (a) }{ \sin (a) - \cos(a) } + \frac{ \cos {}^{2} (a) }{ \cos(a) - \sin(a) } \\ = \frac{ \cos {}^{2} (a) - \sin {}^{2} (a) }{ - ( \sin(a) - \cos(a) } \\ = \frac{ \sin {}^{2} (a) - \cos {}^{2} (a) }{ \sin(a) - \cos(a) } \\ = sin(a) +cos(a)$

sin(a) +cos(a) is the answer hope it's helps option c

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Answer 2

Answer:

$\frac{ \sin(a) }{1 - \cot(a) } + \frac{ \cos(a) }{1 - \tan(a) } \\ = \frac{ \sin {}^{2} (a) }{ \sin (a) - \cos(a) } + \frac{ \cos {}^{2} (a) }{ \cos(a) - \sin(a) } \\ = \frac{ \cos {}^{2} (a) - \sin {}^{2} (a) }{ - ( \sin(a) - \cos(a) } \\ = \frac{ \sin {}^{2} (a) - \cos {}^{2} (a) }{ \sin(a) - \cos(a) } \\ = sin(a) +cos(a)$

sin(a) +cos(a) is the answer hope it's helps option c

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