Question

how do you solve sinx = sin(x -pi/2 ) for 0 ≤ x ≤ 2 π .

Answer 1

You may wish to transform \(\sin(x - \pi/2)\) into an equivalent form of cosine, with only x in the argument.

Answer 2

then how would that be??

Answer 3

You can use the expansion of the sine of a difference or you can find the direct identity.

\(\cos(x) = \sin(\pi/2 - x)\)