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Question
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
Solution
Given that cos A + cos B = `1/2`
2 cos `(("A + B")/2) cos (("A - B")/2) = 1/2` ..(1)
Also given that sin A + sin B = `1/4`
2 sin `(("A + B")/2) cos (("A - B")/2) = 1/4` ..(2)
`(2) divide (1)` we get,
`(2 sin (("A + B")/2) cos (("A - B")/2))/(2 cos (("A + B")/2) cos (("A - B")/2)) = (1/4)/(1/2)`
tan `(("A + B")/2)` = `2/4`
∴ tan `(("A + B")/2) = 1/2`
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