Question 1004805
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1. &nbsp;Regarding first part of your question.

You got 

tan(x) = 0. 

The solutions of this equation are &nbsp;x = 0, +/-{{{pi}}}, +/-{{{2pi}}}, +/-{{{3pi}}} , . . . , +/-{{{k*pi}}}, . . . .

Of them, &nbsp;only 0, {{{pi}}} and {{{2pi}}} &nbsp;belong to the segment &nbsp;[{{{0}}}, {{{2pi}}}] &nbsp;that you pointed.

Other values that you are asking about, &nbsp;like {{{pi/2}}}, {{{3pi/2}}}, &nbsp;are not the roots of the equation &nbsp;tan(x) = 0.


2. &nbsp;Moving on to &nbsp;{{{3*sec^2(x)}}} - {{{4}}} = {{{0}}}.

It is &nbsp;{{{sec(x)}}} = +/-{{{2/sqrt(3)}}}, &nbsp;&nbsp;&nbsp;&nbsp;or&nbsp;&nbsp;&nbsp;&nbsp; {{{1/cos(x)}}} = +/-{{{2/sqrt(3)}}} &nbsp;&nbsp;&nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;cos(x) = +/-{{{sqrt(3)/2}}}.

If &nbsp;cos(x) = {{{sqrt(3)/2}}}, &nbsp;then x = {{{pi/6}}} and x = {{{2pi - pi/6}}} = {{{11pi/6}}} are the solutions in the segment &nbsp;[{{{0}}}, {{{2pi}}}].

If &nbsp;cos(x) = -{{{sqrt(3)/2}}}, &nbsp;then x = {{{5pi/6}}} and x = {{{2pi - 5pi/6}}} = {{{7pi/6}}} are the solutions in the segment &nbsp;[{{{0}}}, {{{2pi}}}].


I recommend you to make a sketch of the unit circle, to mark the angles 0°, 30°, 45°, 60° and 90° in it and to write 

the values of sin, cos and tan for these angles.

Then mark all other angles like 120°, 135°, 150°, 180° and so on till 360° and do the same.

After that you will be much more confident in such problems.
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