Question

If tan theta equals to 4 then find the value of 7 sin theta minus 3 cos theta divided by 7 sin theta + 3 cos theta

Answer 1

Step-by-step explanation:

answer as shown above.....answer=25/31

Answer 2

$\dfrac{7\sin \theta-3\cos \theta}{7\sin \theta+3\cos \theta}$ $=\dfrac{25}{31}$

Step-by-step explanation:

We have,

$\tan \theta =4$

To find, the value of $\dfrac{7\sin \theta-3\cos \theta}{7\sin \theta+3\cos \theta}$ = ?

∴ $\dfrac{7\sin \theta-3\cos \theta}{7\sin \theta+3\cos \theta}$

Dividing numerator and denominator by $\cos \theta$, we get

$=\dfrac{7\dfrac{\sin \theta}{\cos \theta} -3\dfrac{\cos \theta}{\cos \theta} }{7\dfrac{\sin \theta}{\cos \theta} +3\dfrac{\cos \theta}{\cos \theta}}$

$=\dfrac{7\tan \theta-3}{7\tan \theta+3}$

Put $\tan \theta =4$, we get

$=\dfrac{7(4)-3}{7(4)+3}$

$=\dfrac{28-3}{28+3}$

$=\dfrac{25}{31}$

∴ $\dfrac{7\sin \theta-3\cos \theta}{7\sin \theta+3\cos \theta}$ $=\dfrac{25}{31}$