“You didn’t memorize steps. You reasoned .” She handed back his paper. “Next time, trust your own brain instead of someone else’s answer key.”
He stood at the board, chalk in hand, sweating. He wrote (\frac{\sin x}{1+\cos x} \cdot \frac{1-\cos x}{1-\cos x}). Then (\frac{\sin x(1-\cos x)}{1-\cos^2 x}). Then (\frac{\sin x(1-\cos x)}{\sin^2 x}). Then (\frac{1-\cos x}{\sin x}). Then (\frac{1}{\sin x} - \frac{\cos x}{\sin x} = \csc x - \cot x). Answers For No Joking Around Trigonometric Identities
Leo froze. His copied answer said: Multiply numerator and denominator by (1−cos x) . But he had no idea why. “You didn’t memorize steps
From that day on, he never searched for “answers” again. He became the kid who said, “Let me prove it.” chalk in hand
Leo blinked. “Wait… I did?”