Solution to Problem 0100 | Submultiple Angles

Problem 0100

 

$\left[ {\tan {{(22\frac{1}{2})}^0} + \cot {{(22\frac{1}{2})}^0}} \right]$  এর মান নির্ণয় করো

 

 

 

Solution:

 

মনে করি ${(22\frac{1}{2})^0}$, তাহলে $2\theta={45}^0$

 

[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]