Question

the value of tan 1 tan 2 tan 3 .........tan 89 is
a 1
b -1
c 0
d none of these​

Answer 1

Tan 1 . tan 2 .tan 3 . .......tan 88 . tan 89

=sin1/cos1 .sin 2/cos 2  .  ...sin 45/cos 45 .....sin 88/cos 88 . sin 89/ cos 89

=sin(90-89)/cos 1 . sin(90-88)/cos 2...........sin(90-45)/cos 45.........sin(90-1)/cos89

=cos 89/cos1 .cos 88/cos 2......cos 45/cos 45 ..........cos 1/ cos 89

all the values will get cancelled......and the result will be 1