Find the value of (tan1tan2tan3....... tan89) .
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Answered by
2
the answer should be 1 because if we write tan1 as tan(90-89) then it is equal to cot89 and since cot and tan are reciprocals of each so their product will become 1 and the only left after doing this with every tan will be tan 45 which equals to 1.
Answered by
11
Hey there !!
Answer: 1 .
Step-by-step explanation:
= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan 46 ... tan 87 . tan 88 . tan 89
= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan( 90 - 44 ) ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1)
= tan 1 . tan 2 . tan 3 ...tan44 . tan 45 . cot 44 ... cot 3 . cot 2 . cot 1
= tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 44 . cot 44 . tan 45 ... tan 89 . cot 89
= 1 x 1 x 1 x ... 1 x ... x 1 . [ tan 45 = 1 ] .
= 1 .
Hence, it is solved .
THANKS
#BeBrainly .
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