Question

how to solve this please tell me anyone

Answer 1

We know tan and cot are complimentary to each other.

$\textbf {tan(90-∅)=cot∅}$

1. tan10.tan15.tan75.tan80=1

Solving LHS

→tan(90-80).tan(90-75).tan75.tan80
→cot80.cot75.tan75.tan80

We know tan∅×cot∅=1

So cot80×tan80×cot75×tan75 =1
Hence Proved

2.
tan1.tan2.tan3....................tan87.tan88.tan89.

Using tan(90-∅)=cot∅

so
cot89.cot88.cot87...........tan87.tan88.tan89

We know tan∅×cot∅=1

So the whole exoression counts to 1

3.
cos1.cos2.cos3............cos180°

cos1.cos2.cos3.......cos90.......cos180

We know cos90= 0

So whole exoression counta to zero