# SOLUTION: Solve {{{(sin(x/2))^2-(sin(x))^2=0}}}

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 138824: Solve Answer by jim_thompson5910(28595)   (Show Source): You can put this solution on YOUR website! Start with the given equation Let . So this means that Replace with u and with 2u Rewrite as Replace with Square Factor out Now use the zero product property: ...or... Now let's solve : Take the square root of both sides ...or... Take the arcsine of both sides Since , this means ...or... However, since is not in the interval [0,2), it is not a solution. So the first solution is -------------------------------------------------------------------- Now let's solve : Subtract 1 from both sides Divide both sides by -4 Take the square root of both sides: ...or... So let's solve the first part : ...or... ...or... However since our interval is positive, the negative answer is not in the interval. So another part of the solution is --------------------- Now let's solve the second part : ...or... ...or... So another part of the solution is =============================================== Answer: So all together our solutions are: