Question

The numerical value of $(1+\cot x-\text{cosec}x)(1+\tan x+\sec x)$ is

Answer 1

$(1+\cot x-\text{cosec}x)(1+\tan x+\sec x)=(1+\frac{\cos x}{\sin x}-\frac{1}{\sin x})(1+\frac{\sin x}{\cos x}+\frac{1}{\cos x})=\left(\frac{\sin x+\cos x-1}{\sin x}\right)\left(\frac{\sin x+\cos x+1}{\cos x}\right)=\frac{(\sin x+\cos x{)}^2-1}{\sin x\cos x}=\frac{{\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x-1}{\sin x\cos x}=\frac{2\sin x\cos x}{\sin x\cos x}=2$