Don't get afraid, it will be simplified
tan 6 ∘ × tan 4 2 ∘ × tan 6 6 ∘ × tan 7 8 ∘ = ?
The answer is 1.000.
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4 solutions
Interesting. How did you think of such an approach?
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There are 3 formulas frequently taught to JEE students. It's the application of one of them :
t a n A . t a n ( 6 0 ∘ − A ) . t a n ( 6 0 ∘ + A ) = t a n 3 A s i n A . s i n ( 6 0 ∘ − A ) . s i n ( 6 0 ∘ + A ) = 4 s i n 3 A c o s A . c o s ( 6 0 ∘ − A ) . c o s ( 6 0 ∘ + A ) = 4 c o s 3 A
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sir are there some other important formula's in trignometry...plz tell
its indian mind hahaha
don't understand the point of having decimal
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it's a multiplication point thingy
Question had asked for 3 significant figures
This is sooo confusing( I'm a freshmen)
Beautiful! I was unaware of this identity. Thank you for sharing it!
I understand the solution, but I'm slightly concerned because a calculator I used gave me 1.0000000000030633 even though it should be exactly 1
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Calculators use rounded values - the binary in computers cannot "exactly" represent most numbers. But after the first dozen significant figures, it doesn't usually make much difference. https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/
With three decimals, your calculator rendered the right answer for this problem. Why didn' mine? It rendered 4,7046301094784542335862345374029. The calculator I used belongs to W10 operating system. Mi Android calculator yields exactly 1.
This solution really isn't very helpful. Where does this identity come from? Why is it valid? What do the dots mean in contrast to the multiplication crosses? Which of the terms is transfered into what between lines one and two? So many things missing here...
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The dots are the same as multiplication crosses you just use them instead in higher level math
I think this is a >=5 level problem or, at least, this answer.
best way - use a calculator
My calculator was in radians!😥
Well. I thought it was warmups, though.
had to be a simple answer, and the angles above 45 roughly balanced the ones below - so I guess 1!!
I also imagined it was 1 but the three decimals issue got me to the calculator (and it did yield a wrong answer) 8-(
How can you assume same P, B and H for different angles?
Hey i have simplest solution Tan(6) = cot(84) [ tan(90-a) = cot(a)
According to the situation cot(84) . tan(42) . cot(24) . tan(78) Here a very sweet trick should be applied.
You know that tan(a) = perpendicular/ base or P/B ( say)
Tan(a) =p/b and. Cot(a) = b/ p
Put these values here
cot(84) . tan(42) . cot(24) . tan(78)
(P/B) (B/P) (P/B) (B/P) = 1
Thankyou
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According to that logic,
cot(84) = cot(90-42)
cot(84) = cot(24)
cot(84) = cot(90-78)
84 = 48 = 24 = 12
in fact, cot(anything) = B/P
so every number equals every other number
1 = 1.1 = 12 = 999
If you have a solution then don't post it in some random comments section, post it in the solution thread. Your comment has nothing to do with the parent post.
tan A.tan(60-A). tan(60+A) =tan3A
Complete the solution !!!
Using the trigonometric identity : t a n A . t a n ( 6 0 ∘ − A ) . t a n ( 6 0 ∘ + A ) = t a n 3 A t a n 6 ∘ × t a n 4 2 ∘ × t a n 6 6 ∘ × t a n 7 8 ∘
= t a n 5 4 ∘ t a n 6 ∘ × t a n 5 4 ∘ × t a n 6 6 ∘ . t a n 1 8 ∘ t a n 1 8 ∘ × t a n 4 2 ∘ × t a n 7 8 ∘
= t a n 5 4 ∘ t a n ( 3 × 6 ∘ ) . t a n 1 8 ∘ t a n ( 3 × 1 8 ∘ )
= t a n 5 4 ∘ t a n 1 8 ∘ . t a n 1 8 ∘ t a n 5 4 ∘
= 1 . 0 0 0
enjoy !