Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If sin x + sin y = a & cos x + cos y = b, then which of the following may be true.
A
sin (x + y) = 
B
tan 
= 
=
C
tan 
= – 
= –
D
cos (x + y) = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,c)
sinx + sin y = a .....(1)
cosx + cos y = b.....(2)
= 
⇒ tan 
= 
⇒ sin 
= 
, cos 
= 
⇒ sin (x + y) = 2 sin 
cos 
= 
Now for tan 
⇒ (1) 2 + (2) 2 ⇒ 1 + 1 + 2 cos (x – y) = a 2 + b 2
cos (x – y) = 
tan 2 
= 
⇒ tan 2 
= 
⇒ tan 
= ± 
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