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Question
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Solution
tan (x + y) + tan (x – y) = x
Differentiating with respect to x
`sec^2 (x + y) (1 + ("d"y)/("d"x)) + sec^2 (x - y) (1 - ("d"y)/("d"x))` = 1
`sec^2 (x + y) + sec^2 (x + y) ("d"y)/("d"x) + sec^2 (x - y) - sec^2 (x - y) ("d"y)/("d"x)` = 1
`[sec^2 (x + y) - sec^2 (x - y)] ("d"y)/("d"x) = 1 sec^2 (x + y) - sec^2 (x - y)`
`("d"y)/("d"x) = (1 - sec^2 (x + y) - sec^2 (x - y))/(se^2 (x + y) - sec^2 (x - y)`
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