Evaluate : `tan7^0tan23^0tan60^0tan67^0tan83^0`

Explanation

`tan 7^circ tan 23^circ tan 60^circ tan 67^circ tan 83^circ`


As knows,


`tan (90-theta)=cot theta and cot theta=frac{1}{tan theta}`


`tan 7^circ=tan (90^circ-83^circ)=cot 83^circ `


`tan 23^circ=tan (90^circ-67^circ)=cot 67^circ`


Hence, `tan 7^circ tan 23^circ tan 60^circ tan 67^circ tan 83^circ`


`=cot 83^circ cot 67^circ tan 60^circ tan 67^circ tan 83^circ`


`=frac{1}{tan 83^circ} frac{1}{tan 67^circ} tan 60^circ tan 67^circ tan 83^circ`


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