What is the value of the following expression?
(tan 2°tan 88°) (tan 3° tan 87°).....(tan 43° tan47°) tan 45°

(tan 2°tan 88°) (tan 3° tan 87°).....(tan 43° tan47°) tan 45°

complementary angles:

$$\tan x \times \tan (90^\circ - x) = 1$$​ 

 $$\tan 45^\circ = 1$$​  

Solution:
Each pair $$(\tan 2^\circ \tan 88^\circ) (\tan 3^\circ \tan 87^\circ)...(\tan 43^\circ \tan 47^\circ)$$ forms the complementary angles , So;

the value of each pair is  1. 

So the value of expression is: 
= $$1 \times 1 \times \dots \times \tan 45^\circ = \bf 1$$​