Q94 / 160 · AP EAMCET 2020 (18 Sep Shift 1) · Mathematics

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

  • A
    \(\sin (x)\)
  • B
    \(\cos (x)\)
  • Correct answer
    C
    \(\tan (x)\)
  • D
    \(\operatorname{cosec}(x)\)

Solution

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

Hence, the correct answer is option: 'C'.

Relevant Questions