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Question
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
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Solution
a cos (x + y) = b cos (x – y)
a [cos x cos y – sin x sin y] = b [cos x cos y + sin x sin y]
a cos x cos y – a sin x sin y = b cos x cos y + b sin x sin y
a cos x cos y – b cos x cos y = a sin x sin y + b sin x sin y
(a – b) cos x cos y = (a + b) sin x sin y
`("a" - "b") cosy/siny = ("a" + "b") sinx/cosx`
(a – b) cot y = (a + b) tan x
(a + b) tan x = (a – b) cot y .
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