First slide

Trigonometric equations

Question

Let $θ \in [0, 4 π]$ satisfy the equation $(\sin θ + 2) (\sin θ + 3) (\sin θ + 4) = 6$ .If the sum of all the values of $θ$ is of the form $k π$ , then the value of k is

Moderate

A

6
B

5
C

4
D

2

Solution

$W e h a v e (\sin θ + 2) (\sin θ + 3) (\sin θ + 4) = 6$
$S i n c e - 1 \leq \sin θ \leq 1, L H S \geq 6$
$B u t R H S = 6 \Rightarrow \sin θ = - 1$
$S i n c e θ \in [0, 4 π] \Rightarrow θ = \frac{3 π}{2}, \frac{7 π}{2}$
$∴ s u m o f v a l u e s o f θ = \frac{3 π}{2} + \frac{7 π}{2} = 5 π = kπ \Rightarrow k = 5$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App