Question

If $28\cos A+45\sin A=53$ then $53\sin A=55$.

• A. True
• B. False

Answer 1

The correct option is B False

$28\cos A+45\sin A=53.......\left(i\right)$
$let$
$45\cos A-28\sin A=x.........\left(ii\right)$
$squaringandadding\left(i\right)and\left(ii\right)$
${\cos }^{2}A({28}^2+{45}^2)+{\sin }^{2}A({45}^2+{28}^2)={53}^2+x^2$
$\Rightarrow ({28}^2+{45}^2)({\cos }^{2}A+{\sin }^{2}A)={53}^2+x^2$
$\Rightarrow 2809=2809+x^2$
$\Rightarrow x^2=0$
$x=0$
$pluggingin\left(ii\right)$
$45\cos A-28\sin A=0$
$\Rightarrow 45\cos A=28\sin A$
$\Rightarrow \tan A=\frac{45}{28}$
$\sin A=\frac{45}{53}$
$53\sin A=45$
$HencegivenstatementisFalse$