The maximum and minimum value of 6 sin x cos x + 4 cos 2x are respectively

Question

The maximum and minimum value of 6 sin x cos x + 4 cos 2x are respectively (A) 5, 5 (B) -5, 5 (C) 5, -5 (D) None of these

Tardigrade Admin · Accepted Answer

6 sin x cos x+4 cos 2 x=3 sin 2 x+4 cos 2 x ∴ -√32+42 ≤ 3 sin 2 x+4 cos 2 x ≤ √32+42 ⇒ -5 ≤ 3 sin 2 x+4 cos 2 x ≤ 5 Thus, maximum value is 5 and minimum value is -5 .

Q. The maximum and minimum value of $6 sin x cos x + 4 cos 2 x$ are respectively

$5$ , $5$

$- 5$ , $5$

$5$ , $- 5$

None of these

$6 sin x cos x + 4 cos 2 x = 3 sin 2 x + 4 cos 2 x$
$∴ - 3^{2} + 4^{2} \leq 3 sin 2 x + 4 cos 2 x \leq 3^{2} + 4^{2}$
$\Rightarrow - 5 \leq 3 sin 2 x + 4 cos 2 x \leq 5$
Thus, maximum value is 5 and minimum value is $- 5.$

Q. The maximum and minimum value of 6sinxcosx+4cos2x are respectively

5, 5

−5, 5

5, −5