Let α ± β is not an odd multiple of π . If cos α + cos β = b, sin α + sin β = a, θ = 
and sin 2 θ + cos 2 θ = 1 + 
where n ∈ I, then
(i) Value of n is –
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
cos α + cos β = b
2 cos 
cos 
= b … (i)
Now sin α + sin β = a
2 sin 
cos 
= a … (ii)
Divide (ii) by (i)
tan 
= a/b
⇒ tan θ = a/b
Now sin 2 θ + cos 2 θ = 
+ 
= 
⇒ sin 2 θ + cos 2 θ = 1 – 
⇒ n = –2
Now; cosec n A = x
⇒ sin 2 A = x
∴ sin 3A sin A = 3 sin 2 A – 4 sin 4 A
= 3x – 4x 2 So degree is p = 2
∴ maximum value of (p+1) sin x + (p + 2) cos x
= 
= 5 = p + 3
(ii)
cos α + cos β = b
2 cos 
cos 
= b … (i)
Now sin α + sin β = a
2 sin 
cos 
= a … (ii)
Divide (ii) by (i)
tan 
= a/b
⇒ tan θ = a/b
Now sin 2 θ + cos 2 θ = 
+ 
= 
⇒ sin 2 θ + cos 2 θ = 1 – 
⇒ n = –2
Now; cosec
n A = x
⇒ sin 2 A = x
∴ sin 3A sin A = 3 sin 2 A – 4 sin 4 A
= 3x – 4x 2 So degree is p = 2
∴ maximum value of (p+1) sin x + (p + 2) cos x
= 
= 5 = p + 3
(iii)
Sol. cos α + cos β = b
2 cos 
cos 
= b … (i)
Now sin α + sin β = a
2 sin 
cos 
= a … (ii)
Divide (ii) by (i) tan 
= a/b
⇒ tan θ = a/b
Now sin 2 θ + cos 2 θ = 
+ 
= 
⇒ sin 2 θ + cos 2 θ = 1 – 
⇒ n = –2
Now; cosec
n A = x
⇒ sin 2 A = x
∴ sin 3A sin A = 3 sin 2 A – 4 sin 4 A
= 3x – 4x 2 So degree is p = 2
∴ maximum value of (p+1) sin x + (p + 2) cos x
= 
= 5 = p + 3
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