Question

Find the solutions to the given trig equation for 0 < x < 2π: tanx(cosx)=cosx

Answer 1

If tan(x)·cos(x) = cos(x),

then tan(x) = cos(x) / cos(x) = 1

The angles whose tangent is ' 1 ' are 45° and 225° .

Answer 2

$0 \leq x\leq2\pi\ and\ x\neq\frac{\pi}{2}\ and\ x\neq\frac{3\pi}{2}\\\\tanx\cdot cosx=cosx\\\\tanx\cdot cosx-cosx=0\\\\cosx(tanx-1)=0\iff cosx=0\ \vee\ tanx=1\\\\x=\frac{\pi}{2}\notin D\ \vee\ x=\frac{3\pi}{2}\notin D\ \vee\ x=\frac{\pi}{4}\in D\ \vee\ x=\frac{5\pi}{4}\in D$