Let a = 2 x1 + x + x and b = c1 + x. Then a = b, if c = ?

Answer: Option B

$$\begin{array}{rl}& b=\frac{c}{1+\sin x}\\ & \text{Go through option from option B}\\ & b=\frac{1+\sin x-\cos x}{1+\sin x}\\ & =\frac{{\left(1+\sin x\right)}^2-{\cos }^{2}x}{1+\sin x\left(1+\sin x+\cos x\right)}\\ & =\frac{1+{\sin }^{2}x+2{\sin }^{2}x-1+{\sin }^{2}x}{\left(1+\sin x\right)\left(1+\sin x+\cos x\right)}\\ & =\frac{2{\sin }^{2}x+2\sin x}{\left(1+\sin x\right)\left(1+\sin x+\cos x\right)}\\ & =\frac{2\sin x\left(\sin x+1\right)}{1+\sin x+\cos x}\\ & =\frac{2\sin x}{1+\sin x+\cos x}\\ & =a\end{array}$$