Let $A_1$ be the area of the region bounded by the curves $y=\sin x,y=\cos x$ and $y$-axis in the first quadrant. Also, let $A_2$ be the area of the region bounded by the curves $y=\sin x,y=\cos x$, $x$-axis and $x=\frac{\pi }{2}$ in the first quadrant. Then,

• A

  $2A_1=A_2$ and $A_1+A_2=1+\sqrt{2}$
• Correct answer
  B

  $A_1:A_2=1:\sqrt{2}$ and $A_1+A_2=1$
• C

  $A_1:A_2=1:2$ and $A_1+A_2=1$
• D

  $A_1=A_2$ and $A_1+A_2=\sqrt{2}$

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