The number of solution of equation `tanx+secx=2cosx` lying in the interval `[-pi,3pi]` is

Answer

4

Explanation

Now `tanx+secx=2cosx`
`implies(sinx)/(cosx)+(1)/(cosx)=2cosximpliesinx+1=2cos^(2)x`
`impliessinx+1=2(1-sin^(2)x)`
`implies2sin^(2)x+sinx-1=0`
`implies(1+sinx)(2sinx-1)=0`
`impliessinx=(1)/(2),sinx=-1`
but `sinx=-1` does not satisfy the equation
`x=(pi)/(6),(5pi)/(6),2pi+(pi)/(6),3pi-(pi)/(6)` in `[-pi,3pi]`