Problem 0100
[tex]\left[ {\tan {{(22\frac{1}{2})}^0} + \cot {{(22\frac{1}{2})}^0}} \right][/tex] এর মান নির্ণয় করো
Solution:
মনে করি [tex]{(22\frac{1}{2})^0}[/tex], তাহলে [tex]2\theta={45}^0[/tex]
[tex]\begin{array}{l}
\tan {(22\frac{1}{2})^0} + \cot {(22\frac{1}{2})^0}\\ = \tan \theta + \cot \theta \\ = \frac{{\sin \theta }}{{\cos \theta }} + \frac{{\cos \theta }}{{\sin \theta }}\\ = \frac{{{{\sin }^2}\theta + \cos {}^2\theta }}{{\sin \theta \cos \theta }}\\ = \frac{1}{{\sin \theta \cos \theta }}\\ = \frac{2}{{2\sin \theta \cos \theta }}\\ = \frac{2}{{\sin 2\theta }}\\ = \frac{2}{{\sin {{45}^0}}}\\ = \frac{2}{{\frac{1}{{\sqrt 2 }}}}\\ = 2\sqrt 2 \end{array}[/tex]