Question 27

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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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