1http://en.wikipedia.org/wiki/Quartic_function#Solving_a_quartic_equation
yes it is getting messy
waiting for a good solution
If sinx+tanx=5/6 find sinx*tanx.
By converting everything to sinx we get a quartic equation but how to solve that?
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16 Answers
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341If that is the question another way would be
\sec x - \tan x = \frac{1}{\sec x + \tan x} = \frac{6}{5}
and then use
(\sec x + \tan x)^2 - (\sec x - \tan x)^2 = 4\sec x \tan x
11@hemang-If it's true that the question is for secx+tanx=5/6, then you tired a lot of people out on this one.
3here is what i got from someone.
Let tan(x2) = t so sin(x) = 2t 1+t2 and tan(x) = 2t 1-t2
We are given
2t ( 11 + t2 + 11+t2) = 56 =
4t1-t4
implies 5t4+24t =5
And we seek
4t21-t4 = 5t6
where t is root of:
5t4+ 24 t - 5 = 0
(Values about 0.208 and -1.751)
So answer would be around .173 and -1.46..
11But how can we solve the quartic without the help of a calculator?
1http://www.wolframalpha.com/input/?i=sinx+%2B+tanx+%3D+5%2F6
1from
sinx+tanx=5/6
it can be seen that x<30 deg in fact x should be close to 25 deg.
now sin 25 deg = 0.422
and tan 25 deg = 0.466
so ans should be close to 0.2
( i remember these values as they are quite close )