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1 Answer
Shwetank Mauria
Dec 4, 2017

x=1.8557,2.6117,4.9973,5.7533x=1.8557,2.6117,4.9973,5.7533

Explanation:

tan^2x+4tanx+2=0tan2x+4tanx+2=0 can be solved using binomial formula

tanx=(-4+-sqrt(4^2-4*1*2))/2=(-4+-sqrt8)/2=-2+-sqrt2tanx=−4±√42−4⋅1⋅22=−4±√82=−2±√2

i.e. either tanx=-2+sqrt2=-2+1.4142=-0.5858tanx=−2+√2=−2+1.4142=−0.5858

i.e. x=-0.53x=−0.53 and in [0,2pi}[0,2π} x=3.1416-0.53=2.6117x=3.1416−0.53=2.6117 or x=2.6117+3.1416=5.7533x=2.6117+3.1416=5.7533

and if x=-2-sqrt2=-3.4142x=−2−√2=−3.4142, x=-1.2859x=−1.2859 ans in [0,2pi)[0,2π)

x=3.1416-1.2859=1.8557x=3.1416−1.2859=1.8557 or x=3.1416+1.8557=4.9973x=3.1416+1.8557=4.9973

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