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Trigonometrical Equations
easy
જો $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),$ તો $\cos \left( {\theta - \frac{\pi }{4}} \right) =$
A
$\frac{1}{{2\sqrt 2 }}$
B
$\frac{1}{{\sqrt 2 }}$
C
$\frac{1}{{3\sqrt 2 }}$
D
$\frac{1}{{4\sqrt 2 }}$
Solution
(a) $\tan (\pi \cos \theta ) = \tan \left( {\frac{\pi }{2} – \pi \sin \theta } \right)$
$\therefore $ $\,\sin \theta + \cos \theta = \frac{1}{2}$
$ \Rightarrow \,\cos \left( {\theta – \frac{\pi }{4}} \right) = \frac{1}{{2\sqrt 2 }}$.
Standard 11
Mathematics
