Question

The maximum value of $24\sin \theta +7\cos \theta$ is1

• A. $1$
• B. $24$
• C. $25$
• D. $7$

Answer 1

The correct option is C $25$

We know that the max and min value of $a\cos \theta +b\sin \theta$ are $\sqrt{a^2+b^2}$ and $-\sqrt{a^2+b^2}$

$7\cos \theta +24\sin \theta =\sqrt{7^2+{24}^2}=\sqrt{625}=25$

$=-\sqrt{7^2+{24}^2}=\sqrt{625}=-25$

Hence maximum value $25$