Trigonometric Equations and Inequalities

9000086704

Level: 
A
Identify the optimal substitution which simplifies the following equation as much as possible. \[ \mathop{\mathrm{tg}}\nolimits ^{2}v -\mathop{\mathrm{cotg}}\nolimits ^{-1}v = 2 \]
\(\mathop{\mathrm{tg}}\nolimits v = t\)
\(v^{-1} = t\)
\(\mathop{\mathrm{cotg}}\nolimits v = t\)
Equation is not convenient for a substitution.

9000086707

Level: 
A
Identify the equation which arises from the following equation using an optimal substitution. \[ \mathop{\mathrm{tg}}\nolimits ^{2}y - 2\mathop{\mathrm{tg}}\nolimits y = 3 \]
\(t^{2} - 2t - 3 = 0\)
\(\mathop{\mathrm{tg}}\nolimits t = \frac{3} {2}\)
\(t^{2} = \frac{3} {2}\)
\(\mathop{\mathrm{tg}}\nolimits t = 3\)