# Question #f1f92

Apr 23, 2017

See below.

#### Explanation:

Starting from the LHS.

LHS = $\frac{3 - 4 {\sin}^{2} A}{{\cos}^{2} A}$

$= \frac{3 - \left(3 {\sin}^{2} A + {\sin}^{2} A\right)}{{\cos}^{2} A}$

$= \frac{3 - 3 {\sin}^{2} A - {\sin}^{2} A}{{\cos}^{2} A}$

$= \frac{3 \left(1 - {\sin}^{2} A\right) - {\sin}^{2} A}{{\cos}^{2} A}$

$= \frac{3 {\cos}^{2} A - {\sin}^{2} A}{{\cos}^{2} A}$

$= \frac{3 {\cos}^{2} A}{{\cos}^{2} A} - \frac{{\sin}^{2} A}{{\cos}^{2} A}$

$= 3 - {\tan}^{2} A$ = RHS

Apr 24, 2017

LHS = $\frac{3 - 4 {\sin}^{2} A}{{\cos}^{2} A}$

= $\frac{3}{\cos} ^ 2 A - \frac{4 {\sin}^{2} A}{\cos} ^ 2 A$

= $3 {\sec}^{2} A - 4 {\tan}^{2} A$

= $3 \left(1 + {\tan}^{2} A\right) - 4 {\tan}^{2} A$

= $3 + 3 {\tan}^{2} A - 4 {\tan}^{2} A$

= $3 - {\tan}^{2} A = R H S$