The expression solved equals what?

sin^{2}θ - 4 + cos^{2}θ

Notice that there is a trigonometric identity within this expression, that being the pythagorean trig identity which states that following: sin^{2}θ + cos^{2}θ = 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.

Therefore,

sin^{2}θ - 4 + cos^{2}θ <==> (sin^{2}θ + cos^{2}θ) - 4 = 1 - 4 = -3

## Comments

So sin2(T)+cos2(T)=1 is an identity and,

something a student should simply memorize?

You should absolutely memorize this identity, you will use it for your entire mathematical career.