Question

The minimum value of 3cosx + 4sinx + 5 is 5

Option 1)

5

Option 2)

9

Option 3)

7

Option 4)

0

✨ Free AI Tools for You

Powered by Chatterbot AI

Answer

:

The correct option is 4) 0

To determine the minimum value of the expression $3 \cos x + 4 \sin x + 5$, we first need to find the minimum value of $3 \cos x + 4 \sin x$.

Using the formula for the minimum value of an expression of the form $a \cos x + b \sin x$, we get: $$ -\sqrt{a^2 + b^2} $$

In our case: $$ a = 3 \quad \text{and} \quad b = 4 $$

Thus: $$ -\sqrt{3^2 + 4^2} = -\sqrt{9 + 16} = -\sqrt{25} = -5 $$

Therefore, the minimum value of $3 \cos x + 4 \sin x$ is –5.

To find the minimum value of $3 \cos x + 4 \sin x + 5$, we add 5 to the minimum value obtained: $$ -5 + 5 = 0 $$

Hence, the minimum value of $3 \cos x + 4 \sin x + 5$ is 0.


Was this helpful?

India's 1st AI Doubt Solver for CBSE, JEE, and NEET

Ask a Question for Free

and then it's just ₹212 a month