Inactive Tutor answered • 04/14/15
Tutor
New to Wyzant
Can't we also set the other factor equal to zero, so: sin(x) - cos(x) = 0 Moving the cosine to the other side: sin(x) = cos(x) Aren't there angles where the sine of x is equal to the cosine of x?
Inactive Tutor
Yes, there is one more solution to this problems as Michael W mentioned.
The angle that makes sin(x) = cos(x) is 45 degrees, or π/4. This is because when one angle of a right triangle is 45 degrees, the triangle is an isosceles right triangle. The two legs have the same length, making sine and cosine equal to each other.
The other solution is
x = π/4
In addition, neglect π and 2π from the solution. Although, these two solutions are generally true, they do not fall in the boundary
0 ≤ x ≤ π/2 as specified in the question.
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04/14/15
Inactive Tutor
04/14/15