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Question Number 164530 by hoochhoch last updated on 18/Jan/22

Commented by Rasheed.Sindhi last updated on 18/Jan/22

$$\text{You can't use 'macro parameter character \#' in math mode}$$

Answered by Rasheed.Sindhi last updated on 18/Jan/22

$$\sin \alpha =\frac{3}{5};\frac{\cot \alpha +\tan \alpha }{\cot \alpha -\tan \alpha }=?$$$$\frac{\cot \alpha +\tan \alpha }{\cot \alpha -\tan \alpha }=\frac{\frac{\cos \alpha }{\sin \alpha }+\frac{\sin \alpha }{\cos \alpha }}{\frac{\cos \alpha }{\sin \alpha }-\frac{\sin \alpha }{\cos \alpha }}$$$$=\frac{{\cos }^2\alpha +{\sin }^2\alpha }{{\cos }^2\alpha -{\sin }^2\alpha }=\frac{1}{1-{2\sin }^2\alpha }$$$$=\frac{1}{1-2{\left(\frac{3}{5}\right)}^2}=\frac{1}{\frac{25-18}{25}}=\frac{25}{7}$$

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