The simple value of tan 1°. tan 2°. tan 3° ..................... tan 89° is

Given , tan 1°. tan 2°. tan 3° ..................... tan 89°
But tan 89° can be written as tan(90-1)=cot 1 tan(90-theta)=cot(theta) .Similarly
tan 88 =cot 2
tan 87= cot 3................up to tan 46=cot 44
But the centre term tan45° is left over because total no. of terms is odd . Also tan 45 =1 .
Hence, tan1°.tan2°...........tan44°.tan 45°.cot44°..............cot1°
tan and cot with same value cancel out each other.
so ....remaining is tan45°
Hence, the answer is 1.