Trigonometry Crush 7
A = tan ( 6 ∘ ) tan ( 4 2 ∘ ) , B = cot ( 6 6 ∘ ) cot ( 7 8 ∘ )
Which of these numbers are larger?
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3 solutions
Amazing solution to a good problem.....upvoted
Brilliant solution, Raj.
Good use of a nice identity. Good work @Raj Rajput . upvoted!!
But if we use calculator we get a different answer????
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But why you are approaching this with calculator ? Anyways we get same answer from calculator also :)
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will you post it pls
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@Riddhesh Deshmukh – ya use scientific calculator for getting values of tan6 and tan42 then for cot convert it into tan form using 90-(angle) then calculate and then divide you will get it :)
Awesome work as always dude.Upvoted!
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Thanks :) but i didn't get your upvote lol :)
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lol sorry about that.Now i can say Upvoted! :)
Let t = 1 5 π = 1 2 o throughout. We need to show that tan ( t ) tan ( 2 t ) tan ( 4 t ) tan ( 7 t ) = 1 . We have the product formulas ∏ k = 1 7 tan ( k t ) = 1 5 and ∏ k = 1 2 tan ( 3 k t ) = 5 . If we divide the first equation by the second and also by tan ( π / 3 ) = 3 , the claim follows.
Challenge Master Note: WOW How did you know what angles and products to use?
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As you know, I try to solve all trigonometry problems this way. These product formulas for sin, cos, and tan are basically all the trig identities I know ;)
