Question

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

Answer 1

Solution :-

$tan1.tan2.tan\mathrm{3...}tan89$

$tan1.tan2.tan\mathrm{3...}tan(90-3).tan(90-2).tan(90-1)$

$=tan1.tan2.tan\mathrm{3...}cot3.cot2.cot1$

$=1$