Question

If 4 cos x =11 sin x, Find the value of$\frac{11cosx-7sinx}{11cosx+7sin{x}^{\prime }}$

Answer 1

We have

$4\cos x=11\sin x$

$4\left(\frac{\cos x}{\cos x}\right)=11\left(\frac{\sin x}{\cos x}\right)$

$4=11\tan x$

$\tan x=\frac{4}{11}$ ... (1)

Now, $\frac{11\cos x-7\sin x}{11\cos x+7\sin x}=\frac{11\left(\frac{\cos x}{\cos x}\right)-7\left(\frac{\sin x}{\cos x}\right)}{11\left(\frac{\cos x}{\sin x}\right)+7\left(\frac{\sin x}{\cos x}\right)}$

[dividing numerator and denominator by cos x]

$=\frac{11-7\tan x}{11+7\tan x}=\frac{11-7\left(\frac{4}{11}\right)}{11+7\left(\frac{4}{11}\right)}=\frac{11-\frac{28}{11}}{11+\frac{28}{11}}=\frac{121-28}{121+28}=\frac{93}{149}$