Question

Show that $\tan 1^o\tan 2^o\tan 3^o......\tan {89}^o=1$

Answer 1

$tan1\ast tan\mathrm{2......}tan\mathrm{45.....}tan88\ast tan89$

$tan1\ast tan\mathrm{2....}tan\mathrm{45....}cot2\ast cot1$

$Weknowthat:-tanA\ast cotA=1$

$so,1^{4}4\ast tan45$

=$1\ast 1$

$=1$