Practicing Success
If $cos θ + sin θ = \sqrt{2} cos θ$, find the value of $(cos θ − sin θ)$. |
$\sqrt{2} sinθ$ $\sqrt{2} cos θ$ $\frac{1}{\sqrt{2}} sinθ$ $\frac{1}{2} cos θ$ |
$\sqrt{2} sinθ$ |
cos θ + sin θ = √2 . cosθ ----(1) on squaring both side , cos² θ + sin² θ + 2cos θ.sin θ = 2 . cos²θ 2cos θ.sin θ = cos²θ- sin²θ 2cos θ.sin θ = ( cosθ - sinθ ) . ( cosθ + sinθ ) By using equation 1 , 2cos θ.sin θ = ( cosθ - sinθ ) . √2 . cosθ cosθ - sinθ = \(\frac{2cos θ.sin θ}{√2 . cosθ}\) cosθ - sinθ = √2 . sinθ |