Question

The complete solution of the inequality sec^2 3x < 2

Answer 1

Answer:

Correct answer is  x ∈ nπ/3 - π/12 , nπ/3 + π/12

Step-by-step explanation:

sec^2 3x < 2

⇒ sec² 3x - 2 < 0

⇒ ( sec 3x - √2 ) ( sec 3x + √2 ) < 0  [ we know that  a² - b² = (a + b ) ( a - b ) ]  

so, we can write  -√2 < sec 3x < √2

           |          |

           |     |     |    3π/4

----------|----|----|------|---------

            |    π/3         |

            |                  |

  3x ∈ nπ - π/4 , nπ + π/4

⇒ x ∈ nπ/3 - π/12 , nπ/3 + π/12