The value of x for the maximum value of -3cos x-sin x is

The correct option is A 300 Let f(x) = √(3) cos x + sin x ⇒ f(x) = 2( √(3)/2 cos x + 1/2 sin x) = 2 sin (x + π/3) But 1 ≤ sin (x + π/3) ≤ 1 Hence, f(x) is ma ...

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Standard XI

Mathematics

Basic Trigonometric Identities

The value of ...

Question

The value of x for the maximum value of $\sqrt{3} c o s x + s i n x$ is

30⁰

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45⁰

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60⁰

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90⁰

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Solution

The correct option is A
30⁰

Let f(x) = $\sqrt{3} c o s x + s i n x$

$\Rightarrow$ f(x) = 2 $(\frac{\sqrt{3}}{2} c o s x + \frac{1}{2} s i n x)$ = $2 s i n (x + \frac{π}{3})$

But -1 $\leq$ $s i n (x + \frac{π}{3})$ $\leq$ 1

Hence, f(x) is maximum, if x + $\frac{π}{3}$ = $90^{\circ}$ $\Rightarrow$ x = $30^{\circ}$ .

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The value of x for the maximum value of √3cosx+sinx is

The correct option is A 300 Let f(x) = √3cosx+sinx ⇒ f(x) = 2(√32cosx+12sinx) = 2sin(x+π3) But -1 ≤ sin(x+π3) ≤ 1 Hence, f(x) is maximum, if x + π3 = 90∘ ⇒ x = 30∘.

The value of x for the maximum value of $\sqrt{3} c o s x + s i n x$ is