Find all the angles, in terms of pi, for 0<x<5 which satisfy the equation
sin2x=sin(x-4)
Hello acc100jtIn general, if $\displaystyle \sin A = \sin B$, then $\displaystyle A = n\pi + (-1)^nB$
For example, when $\displaystyle n=0, A =B$
When $\displaystyle n = 1, A = \pi - B$
When $\displaystyle n = 2, A = 2\pi + B$
When $\displaystyle n = -1, A = -\pi - B$
... and so on.
So, what you have to do is to solve the equation $\displaystyle 2x = n\pi +(-1)^n(x-4) $ for all the values of $\displaystyle n$ that give values of $\displaystyle x$ in the required range.
So try the values of $\displaystyle n$ that I've given above: $\displaystyle 0, 1, 2, -1,$ ...etc and see what happens.
Grandad