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
Sean
Jan 1, 2018

No solution.

Explanation:

.

#tanxcosxsinx-1=0#

#sinx/cosxcosxsinx-1=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.

Related questions
Impact of this question
1719 views around the world
You can reuse this answer
Creative Commons License