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.

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