Trigonometric equations and inequalities

1003085908

Level: 
C
The solution set of the inequality \( \mathrm{cotg}\left(3x -\frac{\pi}4 \right) \geq -1 \) for \( x\in\left[0;\frac{\pi}2\right] \) is:
\( \{0\}\cup\left( \frac{\pi}{12};\frac{\pi}3 \right]\cup\left(\frac{5\pi}{12};\frac{\pi}2\right] \)
\( \left[ 0;\frac{\pi}3\right] \)
\( \left( \frac{\pi}{12};\frac{\pi}3\right] \)
\( \left( 0;\frac{\pi}2\right] \)

1003085909

Level: 
C
The solution set of the inequality \( |\mathrm{tg}\,x| < 1 \) for \( x\in\left(-\frac{\pi}2;\frac{\pi}2\right) \) is:
\( \left( -\frac{\pi}4;\frac{\pi}4 \right) \)
\( \left( -\frac{\pi}2;\frac{\pi}2 \right) \)
\( \left( 0;\frac{\pi}4 \right) \)
\( \left( -\frac{\pi}2;-\frac{\pi}4 \right) \)

1003085910

Level: 
C
The solution set of the inequality \( \mathrm{tg}^3x + \mathrm{tg}^2x - \mathrm{tg}\,x - 1 < 0 \) for \( x\in\left(-\frac{\pi}2;\frac{\pi}2\right) \) is:
\( \left(-\frac{\pi}2;\frac{\pi}4\right) \)
\( \left(\frac{\pi}2;\frac{7\pi}4\right) \)
\( \left(-\frac{\pi}2;\frac{3\pi}4\right) \)
\( \left(-\frac{\pi}2;\frac{\pi}2\right) \)

1003086007

Level: 
C
The solution set of the equation \( \sin^4x = 1 - \cos^2x \) for \( x\in\left[0^{\circ};360^{\circ}\right] \) is:
\( \left\{0^{\circ};90^{\circ};180^{\circ};270^{\circ};360^{\circ} \right\} \)
\( \left\{0^{\circ};180^{\circ};360^{\circ} \right\} \)
\( \left\{0^{\circ};90^{\circ};270^{\circ};360^{\circ} \right\} \)
\( \left\{90^{\circ};270^{\circ}\right\} \)