need help with these questions -
solve sin(2x-45) = √ 3 / 2
and
find general solutions of sin2x=cosx
thankyou in advance
$\displaystyle \displaystyle \begin{align*} \sin{(2x - 45)} &= \frac{\sqrt{3}}{2} \\ 2x - 45 &= \left\{ 60, 120 \right\} + 360n , n \in \mathbf{Z} \end{align*}$
Go from here.
$\displaystyle \displaystyle \begin{align*} \sin{2x} &= \cos{x} \\ 2\sin{x}\cos{x} &= \cos{x} \\ 2\sin{x}\cos{x} - \cos{x} &= 0 \\ \cos{x}\left(2\sin{x} - 1\right) &= 0 \\ \cos{x} = 0 \textrm{ or } 2\sin{x} - 1 &= 0 \end{align*}$
Go from here.