Question

A student solved the equation sin 2 x / cos x =2,0<x<π. Describe the students error

Answer 1

The student's error is that they did not correctly simplify the equation before attempting to solve it. The correct way to simplify the equation sin 2x / cos x = 2 is to first use the double angle identities to rewrite sin 2x as 2sinx cosx, giving the equation 2sinx cosx / cos x = 2. This can then be simplified to 2sinx = 2, or sinx = 1. Solving for x within the given range of 0 < x < π, the correct solution is x = π/2.