First slide

Trigonometric equations

Question

Sum of integral values of n such that $\sin x (2 \sin x + \cos x) = n$ has at least one real solution is

Moderate

A

1
B

2
C

3
D

0.

Solution

$\begin{array}{l} 2 \sin^{2} x + \frac{2 \sin x \cos x}{2} = n \\ \Rightarrow \sin 2 x + 2 (1 - \cos 2 x) = 2 n \\ \Rightarrow \sin 2 x - 2 \cos 2 x = 2 (n - 1) \\ \Rightarrow - \sqrt{5} \leq 2 n - 2 \leq \sqrt{5} \\ \Rightarrow 1 - \frac{\sqrt{5}}{2} \leq n \leq 1 + \frac{\sqrt{5}}{2} \end{array}$
Integral values of $n$ are $0, 1, 2 .$

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