First slide

Compound angles

Question

Let $0 \leq a, b, c, d \leq π$ where b and c are not complementary such that 2 cos a + 6cos b + 7 cos c + 9 cos d = 0 and
2 sin a -6 sin b + 7 sin c - 9 sin d= 0, then the value of $3 \frac{\cos (a + d)}{\cos (b + c)}$ is

Moderate

Solution

From the given equations, we have
$\begin{aligned} (2 \cos a + 9 \cos d)^{2} = (6 \cos b + 7 \cos c)^{2} \\ and (2 \sin a - 9 \sin d)^{2} = (6 \sin b - 7 \sin c)^{2} \end{aligned}$
Adding, we have 36 cos (a + d)=84 cos(b + c)
or $\frac{\cos (a + d)}{\cos (b + c)} = \frac{7}{3}$

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