Question

Say true or false:
The value of $\sin \theta +\cos \theta$ is always greater than $1$.

• A. True
• B. False

Answer 1

The correct option is B False

Multiplying and dividing by $\sqrt{2}$ we get
$\sqrt{2}[\frac{cos\theta }{\sqrt{2}}+\frac{sin\theta }{\sqrt{2}}]$
$=\sqrt{2}sin(\theta +{45}^0)$
$=\lambda$
For $\theta =-{45}^0$ we have $\lambda =0$
and for $\theta =0$ we have $\lambda =1$
In general
$\lambda =[-\sqrt{2},\sqrt{2}]$
Hence the above statement is false.