Question

Solve the following equations.
$3(cosx-sinx)=1+cos2x-sin2x.$

Answer 1

$3(cosx-sinx)=1+cos2x-sin2x$

$\Rightarrow 3(cosx-sinx)=1+co{s}^{2}x-si{n}^{2}x-2sinx.cosx$

$\Rightarrow 3(cosx-sinx)=2co{s}^{2}x-2sinx.cosx$

$\Rightarrow 3(cosx-sinx)=2cosx[cosx-sinx]$

$\Rightarrow (cosx-sinx)(3-2cosx)=0$

$\therefore cosx=3/2$ or $cos-sinx=0$

(no solution possible) $\Rightarrow tanx=1$

$x=n\pi +\pi /4$

$nϵ$ integer