Solve
(i) 
sin θ – cos θ = 
(ii)5 sin θ + 2 cos θ = 5
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
sin θ – cos θ = 
⇒ 2 
= 
⇒ 2 sin 
= 
⇒ sin 
= 
= sin 
⇒ θ – 
= n π + (–1)n 
.
(ii) 5 sin θ + 2 cos θ = 5 ⇒ 
sin θ + 
cos θ = 
sin φ sin θ + cos φ cos θ = 
⇒ cos ( θ – φ ) = sin φ = cos 
θ – φ = 2n π ± 
⇒ θ = 2n π ± 
φ + φ ⇒ θ = 2n π ± 
, 2n π ± 
+ 2 φ
⇒ θ = 2n π + 
, 2n π – 
+ 2 φ For θ = 2n π – 
+ 2 φ ,
We have θ = 2n π + 2 
= 2n π + 2 
= 2n π + 2 tan–1 
= 2n π + 2 
∴ θ = 2n π + 
or 2n π + 2 α where tan–1 
= α
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