How to Solve Tanx Cosx Sinx-1=0 algebraically, over 0 ≤ x <360 Deg.?

Now the answer says no solution, but I got 90 and 270 Deg for the answers, using Pythagorean identities. So my question is why is that there is no solution? Thanks.

1 Answer
Jan 1, 2018

No solution.

Explanation:

.

tanxcosxsinx-1=0tanxcosxsinx1=0

sinx/cosxcosxsinx-1=0sinxcosxcosxsinx1=0

sinx/cancelcolor(red)cosxcancelcolor(red)cosxsinx-1=0

sin^2x-1=0

sin^2x=1

sinx=+-1

sinx=1, x=90^@

sinx=-1, x=270^@

If we plug our solutions into the original equation since both cos90^@ and cos270^@ are equal to 0 their tan becomes infinity and is considered undefined.

As such, the equation does not hold true. Therefore, there is no solution.