SOLUTION: if 5sin^2 theta+4cos^2 theta=9/2 then tan theta=?

Question 1068990: if 5sin^2 theta+4cos^2 theta=9/2 then tan theta=?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
rewrite as
sin^2 theta + 4 sin^2 theta +4 cos^2 theta=
sin^2 theta+4(sin^2 theta+ cos^2 theta)=sin^2 theta+4=9/2
sin^2 theta=1/2
sin theta= sqrt (2)/2
theta =45 degrees
tan 45=1
check
5(1/2)+4(1/2)=9/2

Answer by ikleyn(52879) (Show Source): You can put this solution on YOUR website!
.
rewrite as
sin^2 theta + 4 sin^2 theta +4 cos^2 theta=
sin^2 theta+4(sin^2 theta+ cos^2 theta)=sin^2 theta+4=9/2
sin^2 theta=1/2 --->

sin theta= +/- sqrt (2)/2
theta = 45�, 135�, 225�, 315�.

Then tan theta = +1 OR -1.

check
5(1/2)+4(1/2)=9/2

The solution by "Boreal" is not exactly/perfectly correct.

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