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Question
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Sum
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Solution
LHS = `(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")`
`= (2 cos ((7"A" + 5"A")/2) cos((7"A" - 5"A")/2))/(2 cos ((7"A" + 5"A")/2) sin((7"A" - 5"A")/2))`
`[∵ cos "C" + cos "D" = 2 cos (("C + D")/2) cos (("C - D")/2)]`
`= (2 cos 6"A" cos "A")/(2 cos 6"A" sin "A")`
`= (cos "A")/(sin "A")`
= cot A = RHS
Hence proved.
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