# True-or-False :If $\tan(\pi \cos \theta)=\cot (\pi \sin \theta)$,then $\cos(\theta-\large\frac{\pi}{4})$$=\pm \large\frac{1}{2\sqrt 2} \begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} ## 1 Answer Need homework help? Click here. \tan (\pi\cos \theta)=\cot (\pi\sin \theta) \tan (\pi\cos \theta)=-\tan (\large\frac{\pi}{2}-$$\pi\sin \theta)$
$\large\frac{\tan (\pi\cos \theta)}{\tan (\Large\frac{\pi}{2}-\normalsize \pi\sin \theta)}$$=-1 If \tan (\pi\cos \theta)=1 then \tan (\large\frac{\pi}{2}$$-\pi\sin \theta)=-1=\tan \large\frac{3\pi}{4}$
$\therefore \pi\cos \theta=\large\frac{\pi}{4}$
$\cos \theta=\large\frac{1}{4}$
$\large\frac{\pi}{2}$$-\pi \sin \theta=\large\frac{3\pi}{4} -\pi \sin \theta=\large\frac{3\pi}{4}-\frac{\pi}{2} -\pi \sin \theta=\large\frac{3\pi-2\pi}{4}=\frac{2\pi}{4} \sin \theta=-\large\frac{1}{4} \tan (\pi\cos \theta)=-1=\tan \large\frac{3\pi}{4} \tan (\large\frac{\pi}{2}$$-\pi\sin\theta)=1=\tan \large\frac{\pi}{4}$
$\pi\cos \theta=\large\frac{3\pi}{4}$
$\cos \theta=\large\frac{3}{4}$
Hence the given statement is true