Imran writes: "sin² A + cos² A = 1, so taking square roots, sin A + cos A = 1." Find sin 45° + cos…

Step 1. The value. $\sin 45^\circ + \cos 45^\circ = \dfrac{2}{\sqrt{2}} = \sqrt{2}$, which is $1.414$.

Step 2. The mistake. The square root of a sum is not the sum of the square roots: $\sqrt{9 + 16} = 5$, but $3 + 4 = 7$.

Step 3. What is true. $(\sin A + \cos A)^2 = 1 + 2\sin A\cos A$, which is more than $1$ for every acute angle.