\(\frac{1-\cos (2 x)+\sin (x)}{\sin (2 x)+\cos (x)}=\)

\(\frac{1-\cos (2 x)+\sin (x)}{\sin (2 x)+\cos (x)}=\)
  1. \(\sin (x)\)
  2. \(\cos (x)\)
  3. \(\tan (x)\)
  4. \(\operatorname{cosec}(x)\)

Solution

\(\begin{aligned} & \frac{1-\cos 2 x+\sin x}{\sin 2 x+\cos x}=\frac{2 \sin ^2 x+\sin x}{2 \sin x \cos x+\cos x} \\ & \frac{\sin x(2 \sin x+1)}{\cos x(2 \sin x+1)}=\tan x. \end{aligned}\)

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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