Login/Sign Up
Prove that f (x) = sin x + √3 cos x has maximum value at x = π/6.
Prove that f (x) = sin x + √3 cos x has maximum value at x = π/6.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Prove that f (x) = sin x + √3 cos x has maximum value at x = π/6.

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 34

Let ∆ABC be the right-angled triangle in which \[\angle B\text{ }=\text{ }{{90}^{o}}\]

Let \[\mathbf{AC}\text{ }=\text{ }\mathbf{x},\text{ }\mathbf{BC}\text{ }=\text{ }\mathbf{y}\]

In this way, \[\mathbf{AB}\text{ }=\text{ }\surd \left( \mathbf{x2}\text{ }+\text{ }\mathbf{y2} \right)\]

\[\angle \mathbf{ACB}\text{ }=\text{ }\mathbf{\theta }\]

\[\mathbf{Let}\text{ }\mathbf{z}\text{ }=\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }\left( \mathbf{given} \right)\]

Presently, the space of \[\mathbf{ABC}\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\mathbf{x}\text{ }\mathbf{AB}\text{ }\mathbf{x}\text{ }\mathbf{BC}\]

 

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 35

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 36

 

Thusly, the space of the given triangle is greatest when the point between its hypotenuse and a side is π/3.

i

More Material