NTA Abhyas JEE Main2020MathematicsTrigonometric Ratios & IdentitiesPractice
If π < θ < 3 π 2 and cos θ = - 3 5 , then t a n θ 4 is equal to
Options
- A5 - 1 2
- B5 + 1 2
- C- 5 + 1 4
- D- 5 - 1 4
Correct answer
B. 5 + 1 2
Step-by-step solution
cos θ = - 3 5 ⇒ 2 c o s 2 θ 2 - 1 = - 3 5 2 c o s 2 θ 2 = 1 - 3 5 = 2 5 c o s θ 2 = ± 1 5 ⇒ c o s θ 2 = - 1 5 ∵ π 2 < θ 2 < 3 π 4 Now, t a n 2 θ 4 = 1 - c o s θ 2 1 + c o s θ 2 = 1 + 1 5 1 - 1 5 = 5 + 1 5 - 1 t a n 2 θ 4 = 5 + 1 2 4 = 5 + 1 2 2 ⇒ t a n θ 4 = 5 + 1 2 ∵ π 4 < θ 4 < 3 π 8