Question

tan1°tan2°tan3°.....tan89°=x

Answer 1

hope this helps you ☺☺☺

Answer 2

If the sum of two agles is 90°. And they are attached to 'tan' then their multiplication will be 1.

For example- tan 30 . tan 60.

you can see the sum of 60 + 30 is 90. And and they are attached with tan. then their multipublication will be equal to 1.

Let's come to the question now.

A series has been given from tan 1 to tan 89. We have to look how many such pairs are there whose angles' sum is 90. And the value of those pairs will be equal to 1.

tan 1 . tan 89 = 1 ( WE already discussed it in the beginning)

tan 2 . tan 88 = 1


tan 3 . tan 87 = 1

Now we cannot keep doing it forever.


tan 44. tan 46. = 1

so we can now put it this way- -

(tan1 tan 89 ) (tan 2 tan 88) ( tan 3 tan 87.).... ..... tan 45

because there is no pair available for tan 45.

You already know the value of ( tan 1 tan 89) is 1 . So replace it with 1.

1 × 1 × 1 ..... tan 45.

tan 45

tan 45 is also 1.

so 1 is your answer.