The maximum value of the function a x+b x is

Correct Answer is : a2+b2{a²+b²}a2+b2

Correct Answer is : a2+b2{a²+b²}a2+b2

Test Index

MHTCET 25 Apr 2025 Shift 1 Paper

Question : 131 of 150

Marks: +1, -0

a \sin x+b \cos x

Solution:

Concept:

The expression

a \sin x + b \cos x

can be written as a single sine function using the auxiliary angle method.

Explanation:

Rewrite the function as

f(x) = a \sin x + b \cos x

Let

r = \sqrt{a^2 + b^2}

and choose an angle

\theta

such that

\cos \theta = \frac{a}{r}

and

\sin \theta = \frac{b}{r}

Substitute these into

f(x)

f(x) = r\left(\cos \theta \sin x + \sin \theta \cos x\right)

f(x) = r \sin(x + \theta)

Since

-1 \le \sin(x + \theta) \le 1

, the maximum value of

r \sin(x + \theta)

r

Thus, the maximum value is

\sqrt{a^2 + b^2}

Answer:

Option A:

\sqrt{a^2 + b^2}

Go to Question:

Prev Question

Next Question