How to solve this equation: secx - cosx = sinx? Thank you!

Question

1608 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-19T19:02:04

$secx - cosx = sinx$

$1/cosx - cosx = sinx$

$(1-cos^2x)/cosx = sinx$

$sin^2x/cosx=sinx$

$sin^2x/cosx-sinx=0$

$(sinx)(sinx/cosx-1)=0$

Here, $sinx=0$ or

$tanx=1$

$x=sin^(-1) 0$ or $x= tan^(-1) 1$

Hence, the general solution would be ${kπ}∪{π/4+kπ},k∈ZZ$