Find the most general solution of the following
(i) sin6x = sin4x – sin2x
(ii) sec4x – sec2x = 2
(iii) tan 
+ tan 
= 2
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) x = 
or x = m π ± 
where m,n ∈ I
(ii) x = (2n+1) 
where n ∈ Ι
(iii) x = m π , m ∈Ι
Sol. (i) sin6x + sin2x – sin4x = 0
2sin4x cos2x – sin4x = 0
⇒ sin 4x = 0 or cos2x = 
⇒ 4x = n π or 2x = 2m π ± 
where m,n ∈ I
⇒ x = 
or x = m π ± 
where m,n ∈ I
(ii) cos2x – cos4x = 2cos2x cos4x ⇒ cos2x –cos4x = cos6x + cos2x
⇒ cos6x + cos4x = 0 ⇒ 2 cos5x cosx = 0 ⇒ cos 5x = 0 or cosx = 0
⇒ 5x = (2n+1) 
or x = (2m+1) 
where m, n ∈ Ι
⇒ x = (2n+1) 
or x = (2m+1) 
where m,n ∈ Ι
(iii) 
⇒ 
⇒ cos2x = 1 ⇒ 2x = 2m π , m ∈ I ⇒ x = m π , m ∈Ι
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