Trigonometric Equations Question 1
Question 1 - 2024 (01 Feb Shift 2)
The number of solutions of the equation $4 \sin ^{2} x-4 \cos ^{3} x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]$ is :
(1) 1
(2) 3
(3) 2
(4) 0
Show Answer
Answer (4)
Solution
$4 \sin ^{2} x-4 \cos ^{3} x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]$
$4-4 \cos ^{2} x-4 \cos ^{3} x+9-4 \cos x=0$
$4 \cos ^{3} x+4 \cos ^{2} x+4 \cos x-13=0$
$4 \cos ^{3} x+4 \cos ^{2} x+4 \cos x=13$
L.H.S. $\leq 12 \mathrm{can}^{\prime} \mathrm{t}$ be equal to 13 .
