Question

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

Answer 1

`0 \leq x\leq2\pi\ and\ x\\eq(\pi)/(2)\ and\ x\\eq(3\pi)/(2)\\\\tanx\cdot cosx=cosx\\\\tanx\cdot cosx-cosx=0\\\\cosx(tanx-1)=0\iff cosx=0\ \vee\ tanx=1\\\\x=(\pi)/(2)\\otin D\ \vee\ x=(3\pi)/(2)\\otin D\ \vee\ x=(\pi)/(4)\in D\ \vee\ x=(5\pi)/(4)\in D`

Answer 2

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° .