यदि `tan 1^(@) tan 2^(@) tan 3^(@) tan 4^(@) …. Tan 89^(@) = x^(2) - 8`, तो x का मान ज्ञात कीजिए |

Explanation

`x^(2) - 8 = (tan 1^(@) tan 89^(@)) ( tan 2^(@) tan 88^(@)) (tan 3^(@) tan 87^(@)) … (tan 44^(@) tan 46^(@)) tan 45^(@)`
`= [tan 1^(@) tan (90^(@) -1^(@))] [tan 2^(@) tan (90^(@) -2^(@))][tan 3^(@) tan (90^(@) -3^(@))]`
`… [tan 44^(@) tan (90^(@) -44^(@))] xx 1`
`(tan 1^(@) cot 1^(@)) (tan 2^(@) cot 2^(@)) (tan 3^(@) cot 3^(@)) .. ( tan 44^(@) cot 44^(@))`
` = 1 xx 1 xx 1 xx ... xx 1`
`rArr x^(2) - 8 = 1`
`rArr x^(2) = 9 " " rArr " " x = pm 3`