Answer all the parts related to the fundamental trigonometric identity.
(i) State the value of sin2θ+cos2θ for any acute angle θ.
(ii) Using the standard trigonometric values for 45∘, verify numerically that the identity obtained in part (i) is true when θ=45∘.
(iii) Consider a right-angled triangle whose hypotenuse has length 1. Explain, with reference to the side lengths of this triangle, why the identity stated in part (i) must hold for every acute angle at the base.