If cos α + cos β = 1/2 and sin α + sin β = 1/3
Column-I | Column-II |
(i) cos = | [A] ± |
(ii) cos = | [B] |
(iii) tan = | [C] |
(iv) tan = | [D] |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) - [B]
(ii) - [C]
(iii)- [A]
(iv)- [D]
Sol. (i) cos α + cos β = ½......(1)
2 cos 
cos 
sin α + sin β = 
........(2)
2sin 
cos 
Divide (2) by (1)
tan 
= 
cos 
= 
2 + 2 cos ( α – β ) = 
cos( α – β ) = 
2 cos 2 
– 1 = cos ( α – β )
2 cos 2 
= ± 
tan 
= ± 
(ii) cos α + cos β = ½
2 cos 
cos 
sin α + sin β = 
2sin 
cos 
Divide (2) by (1)
tan 
= 
cos 
= 
2 + 2 cos ( α – β ) = 
cos( α – β ) = 
2 cos 2 
– 1 = cos ( α – β )
2 cos 2 
= ± 
tan 
= ± 
(iii) cos α + cos β = ½
2 cos 
cos 
sin α + sin β = 
2sin 
cos 
Divide (2) by (1)
tan 
= 
cos 
= 
2 + 2 cos ( α – β ) = 
cos( α – β ) = 
2 cos 2 
– 1 = cos ( α – β )
2 cos 2 
= ± 
tan 
= ± 
(iv) cos α + cos β = ½
2 cos 
cos 
sin α + sin β = 
2sin 
cos 
Divide (2) by (1)
tan 
= 
cos 
= 
2 + 2 cos ( α – β ) = 
cos( α – β ) = 
2 cos 2 
– 1 = cos ( α – β )
2 cos 2 
= ± 
tan 
= ± 
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