the value of (tan1,tan2,tan3,.....tan89is one proof brainliest can solve
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Answered by
15
Given,
tan1°,tan2°...................................tan89°
This's not gcan be rewritten as :
tan1.tan2.tan3...............tan45................tan89
Since,
For instance,
Similarly,we can write the given sequence as :
tan1.tan2.tan3.........tan45................cot3.cot2.cot1
Also,
Thus,all the terms cancel out eachother leaving,
tan45
= 1
Thus,
tan1.tan2.tan3.................tan89 = 1
Answered by
3
Prove that tan 1,tan 2,tan 3.....tan 89 = 1.
Formula :- tan(90 - theta) = cot( theta).
So,
Let us write tan 89, tan 88.... as ...
tan (90 - 89) = cot 1
tan (90 - 88) = cot 2....and so on till tan 46.
So, it becomes...
We also know that :- cot theta is the reciprocal of tan theta.
So,
We can rewrite it as :-
So, only tan 45 will be left.
We know that, tan 45 = 1.
Therefore, our answer is 1.
Hence, proved.
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