Astudent solved the equation sin2x/cosx=2,0< x < pi and found pi/2. describe the students mistake.

The student's mistake is that they did not consider the restrictions innate to the original equation. the entire point of solving an equation is to find a value for a variable that will result in a true statement. looking at the equation    note that when x =  π/2, the denominator becomes cos(π/2), which evaluates to zero. that will be a division by zero, which is undefined. therefore, π/2 is not a solution—it fails to make a true statement.when you solve equations, a good thing to do is to determine restrictions. in this case, cos x cannot be zero:     cos x  ≠ 0which means that x  ≠  π/2 for 0 < x <   π.here is most likely what they attempted:     here, they would have canceled out the cosines.     when they ended up with the final answer of π/2, they should have discarded π/2  from their knowledge of the restrictions. if they did not find restrictions, then they should have at least tried to use it in the original equation. your answer still has to satisfy the original equation; the restrictions you get from the original equation have to remain the same.(the equation has no solution for 0 < x <   π.)

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