Question

If $\text{cosec}\theta =-\sqrt{2}$ and $\tan \theta =-1,\cos \theta$ is

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

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}$

We know that $\sin \left(A\right)=\frac{1}{\text{cosec}A}$
So, $\sin \left(\theta \right)=\frac{1}{\text{cosec}\theta }=\frac{1}{-\sqrt{2}}$
And, $\tan \left(\theta \right)=\frac{\sin \left(\theta \right)}{\cos \left(\theta \right)}=-1$

$\tan \left(\theta \right)=\frac{\frac{1}{-\sqrt{2}}}{\cos \left(\theta \right)}=-1$

$\Rightarrow \cos \left(\theta \right)=\frac{1}{\sqrt{2}}$