Q2. In a Right Angle Triangle ABC Where Angle B is 90 Degrees, how will you Prove that for any of the Acute Angles, say θ in that Triangle: Sin2θ + Cos2θ = 1.
Ans: If B is 90 degrees then the side AC is the hypotenuse of the right-angle triangle. So as per Pythagoras theorem:
AC2 = AB2 + BC2
If we divide each term in the above equation by AC2 we get:
AC2/AC2 = AB2/AC2 + BC2/AC2
I.e (AC/AC)2 = (AB/AC)2 + (BC/AC)2
So, 1 = Cos2θ + Sin2θ, where θ is the angle opposite to side BC.