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`tan 1^@ tan2^@...tan 89^@=`

Answer» We have
`tan 1^@ tan 2^@ tan 3^@.....tan 89^@`
`=tan 1^@tan 2^@.....tan44^@tan 45^@tan 46^@.....tan tan 88^@tan 89^@`
` =(tan 1^@tan 89^@)(tan 2^@.tan 2^@.tan 88^@).....(tan 44^@.tan 46^@).tan 45^@`
`={tan 1^@.tan (90^@-1^@)}.{tan 2^@.tan (90^@-2)}.....{tan 44^@.tan (90^@-44^@)}.tan 45^@`
`=tan 1^@.cot 1^@)(tan 2^@.cot 2^@)......(tan 44^@cot 44^@).1 [because tan (90^@-theta) =cot theta and tan 45^@=1]`
` =1xx1 xx....xx 1 xx 1=1`.


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