Find the solutions. Square root 2*tanx*cosx-tanx

Question

Find the solutions. Square root 2*tanx*cosx-tanx

Answer 1

2*tan(x)*cos(x)-tan(x)=(2*cos(x)-1)*tan(x)=0

 

This equation can now be broken into two:

 

1) tan(x)=0

2) 2*cos(x)-1=0

 

First has solutions: x=π*k, k=0, ±1, ±2, ... or, for short, x=π*k, k∈Z, set of all integers.

 

Second is equivalent to cos(x)=1/2, solution is x=±π/3+2π*k, k∈Z, set of all integers

 

Answer: x=π*k; x=π/3+2π*k; x=-π/3+2π*k, k∈Z, set of all integers.