First slide

Compound angles

Question

In a $Δ P Q R$ , if $3 \sin P + 4 \cos Q = 16$ and $4 \sin Q + 3 \cos P = 1$ , Then the angle R is equal to

Moderate

A

$π / 4$
B

$3 π / 4$
C

$5 π / 6$
D

$π / 6$

Solution

Squaring and adding the given relations we get
$\begin{array}{l} 16 + 9 + 24 \sin (P + Q) = 37 \\ \Rightarrow \sin (P + Q) = 1 / 2 \Rightarrow \sin R = 1 / 2 \end{array}$
$\Rightarrow R = π / 6$ or $5 π / 6$
If $R = 5 π / 6$ , then $P < π / 6 \Rightarrow 3 \sin P < 3 / 2$ .
$\Rightarrow 3 \sin P + 4 \cos Q < 3 / 2 + 4 < 6$
So $R \neq 5 π / 6$

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