Clavis TMUA Set B Paper 2 · Question 7

Here is an attempted proof of the following claim.

If $\sin\theta=\cos\theta$ then $\theta=\frac\pi4$ .

(I) Suppose $\sin\theta=\cos\theta$ .
(II) Squaring both sides gives $\sin^2\theta=\cos^2\theta$ .
(III) Since $\sin^2\theta+\cos^2\theta=1$ , it follows that $2\cos^2\theta=1$ , so $\cos^2\theta=\frac12$ .
(IV) Hence $\cos\theta=\frac1{\sqrt2}$ .
(V) Therefore $\theta=\frac\pi4$ .

Which of the following is the case?

AThe proof is correct.

BThe proof is incorrect, and the first error occurs in line (I).

CThe proof is incorrect, and the first error occurs in line (II).

DThe proof is incorrect, and the first error occurs in line (III).

EThe proof is incorrect, and the first error occurs in line (IV).

FThe proof is incorrect, and the first error occurs in line (V).

examday