AP EAMCET202023 Sep 2020Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If cosec θ + cot θ = 1 3 , then θ lies in the
Options
- A1 st quadrant
- B2 nd quadrant
- C3 rd quadrant
- D4 th
Correct answer
B. 2 nd quadrant
Step-by-step solution
cos e c θ + cot θ = 1 3 ⇒ 1 + cos θ sin θ = 1 3 3 + 3 cos θ = sin θ Squaring 9 cos 2 θ + 18 cos θ + 9 = 1 - cos 2 θ ⇒ 10 cos 2 θ + 18 cos θ + 8 = 0 ⇒ 5 cos 2 θ + 9 cos θ + 4 = 0 ⇒ 5 cos 2 θ + 5 cos θ + 4 cos θ + 4 = 0 ⇒ 5 cos θ ( cos θ + 1 ) + 4 ( cos θ + 1 ) = 0 ⇒ cos θ = - 1 ,   - 4 5 cos θ = - 4 5 → θ lies in 2 nd or 4 th quadrant But cosec θ + cot _