Solve the inequality sin ⁡ ( x ) ⋅ | tan ⁡ x | ≤ 3 2

Question

Solve the inequality   sin  ⁡  (  x  )  ⋅      |    tan  ⁡      x        |    ≤      3    2

Sawyer Day · Accepted Answer

Yes. the equation is equivalent to the couple of systems:

{\begin{cases} \tan x \geq 0 \\ \frac{\sin^{2} x}{\cos x} \leq \frac{3}{2} \end{cases} \lor {\begin{cases} \tan x < 0 \\ - \frac{\sin^{2} x}{\cos x} \leq \frac{3}{2} \end{cases}

Taniyah Estrada · Accepted Answer

Hint:      {                            tan          ⁡          x                          ,          1                      º                    Q                          or                          3                      º                    Q                                      −          tan          ⁡          x                          ,          2                      º                    Q                          or                          4                      º                    Q                        Now solve in each case.1.   1      º    Q or   3      º    Q  3      º    Q1.   2      º    Q or   4      º    Q  −                    sin        2            ⁡      x              cos      ⁡      x        ≤      3    2    →            −      1      +              cos        2            ⁡      x              cos      ⁡      x        ≤      3    2    →            −      2      +      2              cos        2            ⁡      x      −      3      cos      ⁡      x              2      cos      ⁡      x        ≤  0

Solve the inequality sin ⁡ ( x ) ⋅ | tan ⁡ x | ≤...

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