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Trigonometrical Equations
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If $tan(\pi sin \theta)$ $= cot(\pi cos \theta)$, then $\left| {\cot \left( {\theta - \frac{\pi }{4}} \right)} \right|$ is -
A
$\frac{1}{{\sqrt 7 }}$
B
$\sqrt 7$
C
$\frac{2}{{\sqrt 7 }}$
D
$2 \sqrt 7$
Solution
$\frac{\sin (\pi \sin \theta)}{\cos (\pi \sin \theta)}=\frac{\cos (\pi \cos \theta)}{\sin (\pi \cos \theta)}$
$\Rightarrow \cos (\pi \cos \theta+\pi \sin \theta)=0$
$\Rightarrow(\cos \theta+\sin \theta) \pi=\pm \frac{\pi}{2}$
$\Rightarrow \cos \theta+\sin \theta=\pm \frac{1}{2}$
$\Rightarrow \cos \left(\theta-\frac{\pi}{4}\right)=\pm \frac{1}{2 \sqrt{2}}$
$\Rightarrow \cot \left(\theta-\frac{\pi}{4}\right)=\pm \frac{1}{\sqrt{7}}$
Standard 11
Mathematics
