If 7 =4 then (7 -3 ) (7 +3 ) =? - Vidyadip

MCQ

If $7\tan\theta=4$ then $\frac{(7\sin\theta-3\cos\theta)}{(7\sin\theta+3\cos\theta)} =?$

✓
$\frac{1}{7}$
B
$\frac{5}{7}$
C
$\frac{3}{7}$
D
$\frac{5}{14}$

✓

Answer

Correct option: A.

$\frac{1}{7}$

Given, $7\tan\theta=4$
Now, $\frac{(7\sin\theta-3\cos\theta)}{(7\sin\theta+3\cos\theta)} $
$=\frac{\frac{7\sin\theta}{\cos\theta}-\frac{3\cos\theta}{\cos\theta}}{\frac{7\sin\theta}{\cos\theta}+\frac{3\cos\theta}{\cos\theta}}$
$=\frac{7\tan\theta-3}{7\tan\theta+3}$
$=\frac{4-3}{4+3}=\frac{1}{7}$

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