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Show that f(x) = tan–1(sin x + cos x) is an increasing function in (0, π/4).
Show that f(x) = tan–1(sin x + cos x) is an increasing function in (0, π/4).
Application of Derivatives | Class 12 | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Show that f(x) = tan–1(sin x + cos x) is an increasing function in (0, π/4).

Given, \[f\left( x \right)\text{ }=\text{ }tan1\left( sin\text{ }x\text{ }+\text{ }cos\text{ }x \right)\text{ }in\text{ }\left( 0,\text{ }\pi /4 \right).\]

DIFFERENTIATING the two sides w.r.t. x, we got

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 30

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 31

Hence, the given capacity f(x) is an expanding capacity in \[\left( 0,\text{ }\pi /4 \right).\]

i

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