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36 votes
36 votes
Prove that tan² 20° + tan² 40° + tan² 80° = 33

User Lucas Vazquez
by
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1 Answer

18 votes
18 votes
Explanation:
Now we know that
sec?# -tan? e=1
So tanZ0 =sec20 - 1
So the left of the given equation will be
sec220 + sec240 +sec280-3
SO
1/cos220+1/cos249+1/cos280-3
Remember sec 0= 1/cosf
SO
= since sec0 = 1/cos©
we have
= 1.1324 + 1.7040 + 33.1634 - 3
= 35.9998 - 3
= 33
User Thothal
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2.5k points