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Question
If Y = tan-1 `[(cos 2x - sin 2x)/(sin2x + cos 2x)]` then find `(dy)/(dx)`
Solution
Let y = tan-1 `[(cos 2x - sin 2x)/(sin2x + cos 2x)]`
y = tan-1 `[((cos 2x) /(cos 2x)- (sin2x)/(cos 2x))/((sin2x) /(cos 2x)- (cos 2x)/(cos 2x))]`
y = tan-1 `((1 - tan 2x)/(1 + tan 2x))`
y = tan-1 `[(tan π/4 - tan 2x)/(1 + tan π/4. tan 2x)]`
y = tan-1 `[tan ( π/4 - 2x)]`
y = π/4 - 2x
Diff w.r.t.x
`therefore (dy)/(dx) = -2`
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