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2 problems match “tangent addition formula”. Clear

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1. Angle PCQ in a unit square ●●●○○ 50 ptsGiven a square $ABCD$ with side length $1$, points $P$ and $Q$ lie on sides $AB$ and $AD$, respectively. If the perimeter of $\triangle APQ$ is $2$, find the angle $\angle PCQ$ in degrees.
2. Maximum of tan beta under a constraint ●●●○○ 50 ptsGiven $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$ with $\alpha+\beta \neq \frac{\pi}{2}$ and $\sin \beta=2 \cos (\alpha+\beta) \sin \alpha$, find the maximum value of $\tan \beta$. Round to two decimal places.