### Question 15

SSC-CGL 2020 Mar 3 Shift 1

If 6 tan A = 5, then (8 sin A- 4 cos A)/(cos A - 2 sin A) = ?

### Solution in Brief

We have been given tan A = 5/6. Next divide the numerator and denominator of (8 sin A- 4 cos A)/(cos A - 2 sin A) by cos A to get (8 tan A - 4)/(1 - 2 tanA). Now put tan A = 5/6 and simplify to get -4 ans!

### Solution in Detail

Given $\displaystyle 6\tan A = 5$

$\displaystyle \implies \tan A = \frac 56\text{ . . . (1)}$

To find $\displaystyle \frac{8\sin A- 4 \cos A}{\cos A - 2\sin A}$

Divide num and den by $\displaystyle \cos A$

We get $\displaystyle \frac{8\tan A- 4}{1 - 2\tan A}$

by (1), which $\displaystyle = \frac{8 \times (5/6) - 4}{1 - 2 \times (5/6)}$

$\displaystyle = -4 \:\underline{Ans}$

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