problem archive
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Evaluate \( \arctan(1) \) -
Determine \( \arcsin\left( -\frac{\sqrt{3}}{2} \right) \) -
Find \( \arccos\left( -\frac{1}{2} \right) \) -
Solve \( \arctan(x) = \frac{\pi}{4} \) for \( x \) -
Solve for \( x \) in \( \arccos(x) = \frac{\pi}{3} \) -
Solve for \( \theta \) in the equation \( 2 \sin(\theta) - 1 = 0 \) -
Simplify \( \sin(2\theta) + \sin(4\theta) \) -
Solve \( \sin(2x) = \cos(x) \) -
Find the exact value of \( \tan(75^\circ) \) -
Prove the identity \( \cos^2(x) - \sin^2(x) = \cos(2x) \) -
Verify that \( \sin^2(x) + \cos^2(x) = 1 \) -
If \( \sin(x) = \frac{3}{5} \), find \( \cos(x) \) -
Find all solutions to the equation \( \tan^2(x) = 1 \) -
Express \( \sin(x+y) \) in terms of \( \sin(x) \) and \( \cos(y) \) -
Prove \( \sin(x) + \sin(y) = 2 \sin(\frac{x+y}{2}) \cos(\frac{x-y}{2}) \) -
Prove the identity: \( \cos(x) - \cos(3x) = 4 \cos(x) \sin^2(x) \) -
Solve for \( \theta \) in the equation \( \cos(2\theta) = \frac{1}{2} \) for \( 0 \leq \theta < 2\pi \) -
If \( \tan(A) = \frac{1}{3} \) and \( \tan(B) = \frac{1}{2} \), find the value of \( \tan(A + B) \) -
Find all solutions to \( \cos(2x) - \sin^2(x) = 0 \) for \( 0 \leq x < 2\pi \) -
Prove that \( \tan(x) + \cot(x) = \frac{2}{\sin(2x)} \)