The expression solved equals what?
sine^2 theta -4 + cos^2 theta equals what?
sin2θ - 4 + cos2θ
Notice that there is a trigonometric identity within this expression, that being the pythagorean trig identity which states that following: sin2θ + cos2θ = 1
It follows from the pythagorean theorem that if the length of the hypotenuse of a right triangle is 1 then the lengths of the legs are the sine and cosine of one of the angles, which yields the above trig identity that always holds true.
sin2θ - 4 + cos2θ <==> (sin2θ + cos2θ) - 4 = 1 - 4 = -3
we know ... sin2(Θ)+cos2(Θ)=1
so sin2(Θ)+cos2(Θ) -4 = 1 - 4
so the answer is -3