AP EAMCET201921 Apr 2019Evening ShiftMathematicsTrigonometric EquationsActual
If 4 sin 2 x sin 4 x + sin 2 x = 3 , then x =
Options
- A2 n π 3 ± π 9 ,   n ∈ Z
- Bm π 3 ± π 9 ,   n ∈ Z
- Cn π 3 + ( - 1 ) n π 9 ,   n ∈ Z
- Dn π 3 + ( - 1 ) n 2 π 9 ,   n ∈ Z
Correct answer
B. m π 3 ± π 9 ,   n ∈ Z
Step-by-step solution
Simplify the given expression 4 sin 2 x sin 4 x + sin 2 x = 3 ⇒ 2 ( cos 2 x - cos 6 x ) + 2 ( 1 - cos 2 x ) = 3 ⇒ 2 cos 2 x - 2 cos 6 x + 2 - 2 cos 2 x = 3 ⇒ - 2 cos 6 x + 2 = 3 ⇒ cos 6 x = - 1 2 Therefore, 6 x = 2 π n ± 2 π 3 ⇒ x = 2 n π 6 ± 2 6 × π 3 ⇒ x = n π 3 ± π 9