waecmaths question:
if $\tan x=1$evaluate $\sin x+\cos x$ leaving your answer in surd form
Option A:
$2\sqrt{2}$
Option B:
$\tfrac{1}{2}\sqrt{2}$
Option C:
$\sqrt{2}$
Option D:
2
waecmaths solution:
$\begin{align} & \tan x=1 \\ & x={{\tan }^{-1}}(1)={{45}^{\circ }} \\ & \sin x+\cos x=\sin {{45}^{\circ }}+\cos {{45}^{\circ }}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{2}{\sqrt{2}} \\ & \sin x+\cos x=\frac{2}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ & \sin x+\cos x=\frac{2\sqrt{2}}{2}=\sqrt{2} \\\end{align}$
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