How do you solve 3tan^2theta=1?

2 Answers
Narad T.
Feb 10, 2017

The solutions are S={pi/6+kpi , -pi/6+kpi}

Explanation:

3tan^2theta=1

tan^2theta=1/3

tantheta=+-1/sqrt3

tantheta=1/sqrt3

theta=pi/6 +kpi, k in ZZ

tan theta=-1/sqrt3

theta=-pi/6+kpi, kinZZ

Binayaka C.
Feb 10, 2017

General solution: theta = 2npi + (pi/6) , 2n pi+( (7pi)/6) , 2npi + ((5pi)/6) , 2n pi +( (11pi)/6) for [n=0,1,2,3, .........]

Explanation:

3 tan^2 theta = 1 or tan^2 theta = 1/3 or tan theta = +- 1/sqrt 3, tan theta = 1/sqrt 3 ; tan (pi/6) = 1/sqrt 3 ; tan (pi +pi/6) = 1/sqrt 3 :. theta = (pi/6) , theta = ( (7pi)/6)

tan theta = -1/sqrt 3 ; tan (pi -pi/6) = -1/sqrt 3 ; tan ( 2pi -pi/6) = -1/sqrt 3 :. theta = ((5pi)/6) , theta = ( (11pi)/6)

General solution: theta = 2npi + (pi/6) , theta = 2n pi+( (7pi)/6)

and theta = 2npi + ((5pi)/6) , theta = 2n pi +( (11pi)/6)

where n is a whole number as [n=0,1,2,3, .........] [Ans]

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