A) \[\tan \alpha \]
B) \[\cot \alpha \]
C) \[-1\]
D) 1
Correct Answer: C
Solution :
| \[5\alpha =2\alpha +3\alpha \] |
| take tangent both side |
| \[\Rightarrow \]\[\tan 5\,\alpha =\frac{\tan 2\,\alpha +\tan 3\,\alpha }{1-\tan 2\,\alpha \tan 3\,\alpha }\]\[\Rightarrow \]\[\tan 5\,\alpha -\tan 2\alpha \cdot \tan 3\alpha \cdot \tan 5\alpha \]\[=\tan 2\alpha +\tan 3\alpha \] |
| \[\therefore \] \[-1=\frac{\tan 2\alpha +\tan 3\alpha -\tan 5\,\alpha }{tan2\alpha \cdot \tan 3\alpha \cdot \tan 5\,\alpha }\] |
| \[\therefore \] Ans. is C |
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