Function game
f ( x ) = x 2 0 1 5 + 1 2 0 1 5 + x 2 0 1 6 + 1 2 0 1 6 − x 2 0 1 7 + 1 2 0 1 7
Find the value of f ( tan 1 5 ∘ ) + f ( tan 3 0 ∘ ) + f ( tan 4 5 ∘ ) + f ( tan 6 0 ∘ ) + f ( tan 7 5 ∘ ) .
The answer is 5035.
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2 solutions
You want to ask :
f ( x ) = x 2 0 1 5 + 1 2 0 1 5 + x 2 0 1 6 + 1 2 0 1 6 − x 2 0 1 7 + 1 2 0 1 7
f ( tan 1 5 ∘ ) + f ( tan 3 0 ∘ ) + f ( tan 4 5 ∘ ) + f ( tan 6 0 ∘ ) + f ( tan 7 5 ∘ )
= ( 2 0 1 5 + 2 0 1 6 + 2 0 1 7 ) × 2 + 2 2 0 1 5 + 2 0 1 6 − 2 0 1 7 = 5 0 3 5
sorry, i have corrected it,thank you
(2015+2016-2017)(2)+(2015+2016-2017)/2
x m + 1 m + x − m + 1 m = m ( 1 + x m + x − m + 1 x − m + 1 + x m + 1 ) = m . T a n 7 5 = T a n 1 5 1 , T a n 6 0 = T a n 3 0 1 , a n d T a n 4 5 = 1 . ∴ g i v e n e x p r e s s i o n = 2 0 1 5 + 2 0 1 5 + 2 1 ∗ 2 0 1 5 + 2 0 1 6 + 2 0 1 6 + 2 1 ∗ 2 0 1 6 − 2 0 1 7 + 2 0 1 7 + 2 1 ∗ 2 0 1 7 = 2 5 ∗ ( 2 0 1 5 + 2 0 1 6 − 2 0 1 7 = 5 0 3 5 .