Question

If $\tan \theta =1$ and $\sin \varphi =\frac{1}{\sqrt{2}},$ then the value of $\cos (\theta +\varphi )$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

Answer: (B)

$0$

$\tan \theta =1$
$\tan \theta =\tan 45$
$\theta ={45}^{\circ }$
$\sin \varphi =\frac{1}{\sqrt{2}}$
$\sin \varphi =\sin 45$
$\varphi ={45}^{\circ }$
Now, $\cos (\theta +\varphi )=\cos (45+45)=\cos 90=0$