Question

What is the value of( tan 1 °, tan 2°,tan 3°------- tan 89°)

Answer 1

tan1.tan2.........tan89
tan 89 can be written as cot 1[tan(90-1)=cot 1] by tan(90-theta)=cot(theta)

tan(90-89) tan89
=cot89 x tan89
= 1/tan89 x tan89  [tan89 will be canceled on both the sides by multiplying]
=1.

tan(90-88) tan88
cot88 x tan88
1/tan88 x tan88
= 1
the answer will remain one