What is the solution to tan^2x cosx = tan^2x?

Question

I could not get the answer 0 and π

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Answer 1 · 2018-04-17T22:20:39

See method below

#tan^2(x) cos(x) = tan^2(x)#

Let's consider the case where #tan(x)!=0#

Divide both sides by #tan^2(x)#
#cos(x) = 1 => x=0#

Now let's consider the case where #tan(x)=0#

#tan(x)=0 => sin(x)=0#

#cos^2(x) + sin^2(x) = 1#

#cos^2(x) = 1#

#cos(x) = ± 1#

We have already found the solution #cos(x) = 1# but we now have a second solution as well: #cos(x) = -1#

#cos(x) = -1 => x=pi#

So #x=0# or #x=pi#