Question 1088052
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To solve it effectively, you must to know that

{{{sin^2(x) - cos^2(x)}}} = -cos(2x).


It is the direct consequence of the adding formula for cosine.


Then your equations becomes

cos(2x) = 0 

and has the solutions  x = {{{pi/4}}}, {{{3pi/4}}}, {{{5pi/4}}} and {{{7pi/4}}}.
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