Question

Find the value of tan1°.tan2°.tan3°..........tan89°


Your options are A) 0
B) 1
C) 2
D) 1/2

Answer 1

tan(90-1) tan(90-2).....tan45°

cot89 cot88..... tan45

cot89×tan89....1

1×1
the correct option is B.(1)

Answer 2

tan1 tan 89 tan 2 tan 88.........tan 45

Here its odd terms so mid angle would be 45

And here by taking n th term from beginning and end

tan 1 tan(90-1) tan2 tan( 90-2)........tan45

tan 1 cot 1 tan 2 cot 2...........1

tan 1 × 1/tan1 × tan 2 × 1/tan2........

1 × 1×.....


1