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प्रश्न
Differentiate the following w.r.t. x : `tan^-1((cos7x)/(1 + sin7x))`
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उत्तर
Let y = `tan^-1((cos7x)/(1 + sin7x))`
= `tan^-1[(sin(pi/2 - 7x))/(1 + cos(pi/2 - 7x))]`
= `tan^-1[(2sin(pi/4 - (7x)/2).cos(pi/4 - (7x)/2))/(2cos^2(pi/4 - (7x)/2))]`
= `tan^-1[tan(pi/4 - (7x)/2)]`
= `pi/(4) - (7x)/(2)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(pi/4 - (7x)/2)`
= `"d"/"dx"(pi/4) - (7)/(2)"d"/"dx"(x)`
= `0 - (7)/(2) xx 1`
= `-(7)/(2)`.
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