Find the exact value? 3-2sin^2x=3cosx

2 Answers
May 9, 2018

rarrx=2npi+-pi/3 OR x=2npi

Explanation:

rarr3-2sin^2x=3cosx

rarr3-2(1-cos^2x)=3cosx

rarr3-2+2cos^2x=3cosx

rarr2cos^2x-3cosx+1=0

rarr2cos^2x-2cosx-cosx+1=0

rarr2cosx(cosx-1)-1(cosx-1)=0

rarr(2cosx-1)(cosx-1)=0

Either, 2cosx-1=0

rarrcosx=1/2=cos(pi/3)

rarrx=2npi+-pi/3 where nrarrZ

OR, cosx-1=0

rarrcosx=1=cos 0

rarrx=2pi n where nrarrZ

Jun 2, 2018

x = pm 60^circ + 360^circ k or x = 360^circ k quad integer k

Explanation:

The other answer is fine; I just want to add this to my collection of yet anther trig problem that's going to work out to 30/60/90 or 45/45/90. When are we going to realize that it's goofy to teach a subject that only handles two triangles reasonably well?

3 - 2 sin ^2 x = 3 cos x

3 - 2(1 - cos^2 x) =3 cos x

2 cos ^2x - 3 cos x + 1 = 0

(2 cos x - 1 )(cos x - 1) = 0

cos x = 1/2 or cos x = 1

Cosine or sine of 1/2; same old same old.

cos x = cos 60^circ or cos x = cos 0

x = pm 60^circ + 360^circ k or x = 360^circ k quad integer k