Question

if tan theta =1 then sin theta +cos theta =?​

Answer 1

Answer:

$\sqrt{2}$

Step-by-step explanation:

given, tanθ = 1

         => θ = 45°

then, sinθ = sin45° = $\frac{1}{\sqrt{2} }$

and  cosθ = cos45° = $\frac{1}{\sqrt{2} }$

so, sinθ + cosθ = $\frac{1}{\sqrt{2} }$ + $\frac{1}{\sqrt{2} }$

                         = $\frac{\sqrt{2}+\sqrt{2}}{\sqrt{2}*\sqrt{2} }$

                         = $\frac{2\sqrt{2}}{2}$

                         = $\sqrt{2}$