Question 1128160
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<pre>
You are given that  

{{{sin(theta)}}} = x   and  {{{theta}}} is between {{{-pi/2}}}  and  {{{pi/2}}},      (1)

and they want you calculate  {{{tan(theta)}}}.


From (1),  {{{cos(theta)}}} = {{{sqrt(1-sin^2(theta))}}} = {{{sqrt(1-x^2)}}} and  {{{cos(theta)}}}  is positive in the given interval.


So,  {{{tan(theta)}}} = {{{sin(theta)/cos(theta)}}} = {{{x/sqrt(1-x^2)}}}.


Note that  {{{tan(theta)}}} might be positive or negative depending on the sign of "x".
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You may often meet such problems in your school years - so memorize this solution and repeat it as a mantra 
when you will solve similar problem next time.