Discussion
In a right-angled triangle PQR, right angled at Q, if tan P = 1, then the value of 2 sin P cos P is
Answer: D
The value is 1.
tan P = 1 means P = 45°. Then sin P = cos P = \(\frac{1}{\sqrt{2}}\), so
\[ \begin{aligned} 2\sin P\cos P &= 2 \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}} \\ &= 1 \end{aligned} \]
The same follows from the identity 2 sin P cos P = sin 2P = sin 90° = 1. The value \(1/\sqrt{2}\) is sin P alone, \(\sqrt{2}\) is sin P + cos P, and 2 doubles the correct answer.
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