Solve the equation sin 2 4x + cos 2 x = 2 sin 4x . cos 4 x
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
x = (2 n + 1) 
, n ∈ I
sin 2 4x + cos 2 x = 2 sin 4x . cos 4 x
⇒ sin 2 4x – 2sin4xcos 4 x + cos 2 x = 0
⇒ (sin4x – cos 4 x) 2 + cos 2 x – cos 8 x = 0
⇒ (sin4x – cos 4 x) 2 + cos 2 x (1– cos 6 x) = 0
⇒ sin4x – cos 4 x = 0 ..........
and cos 2 x (1– cos 6 x) = 0..........
From cos 2 x = 0, 1
Case- I cos 2 x = 0 ⇒ 
⇒ 4x = 
∴ sin 4x = 0
⇒ equation is also true
Case- II cos 2 x = 1 ⇒ sin 2 x = 0
⇒ x = n π equation becomes
0 – 1 = 0 false solution is 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems