Question

Product tan1°.tan2°.tan3º......tan89° is:

(a) 1
(0) 0
(b)-1
(d) 90

Please answer in a little bit detail ​

Answer 1

`\sin(x) = \cos(90-x) <=> (sin(x))/(cos(90-x)) = 1\\\prod_(n=1)^(89)\tan(n) = (\sin(1))/(\cos(1)) \cdot (sin(2))/(cos(2))...(sin(89))/(cos(89)) = 1`