Question

(1-cosx)(1+1/cosx)= sinx tanx

Answer 1

Explanation:

`(1 - Cos \ x)*(1+(1)/(Cos \ x))=(1- Cos \ x)* \left((Cos \x )/(Cos \ x)+(1)/(Cos \ x) \right)`

`= (1-Cos \ x)*\left((Cos \ x + 1)/(Cos x)\right)\\\\=((1-Cos \ x)(1+Cos \ x))/(Cos \ x)=(1^(2)-Cos^(2) \ x)/(Cos \ x)\\\\=(1 -Cos^(2) \ x)/(Cos \ x)\\\\=(Sin^(2) \ x)/(Cos \ x)\\\\=Sin \ x * ( Sin \ x)/(Cos \ x)\\\\`

= Sin x * Tan x

Hence proved