Solve the following equation
(i) 5 cos2 θ + 2cos 2 
+ 1 = 0, – 
< θ < 
(ii) sin7 θ + sin4 θ + sin θ = 0 , 0 ≤ θ ≤ π
(iii)tan θ + sec θ = 
, 0 ≤ θ ≤ 2 π
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
, 
(ii) 0, 
(iii) 
Sol. (i) 5cos2 θ + 1 + cos θ + 1 = 0
⇒ 10 cos 2 θ + cos θ – 3 = 0
⇒ cos θ = 
and 
(reject)
⇒ θ = 
, 
(ii) sin4 θ + 2sin4 θ × cos3 θ = 0
⇒ sin4 θ = 0 or cos3 θ = 
⇒ 4 θ = 0, π , 2 π , 3 π , 4 π or 3 θ = π – 
, π + 
, 
⇒ θ = 0, 
(iii) sec θ – tan θ = 
⇒ 2tan θ = 
⇒ tan θ = 
⇒ θ = 
(Reject)
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