Question

If 4sin^2a = 1 find the value of 2+3cos^2a/1-2sin^2a

Answer 1

Answer:

$\large \bold\red{ \frac{17}{2} }$

Step-by-step explanation:

Given,

• $4 { \sin }^{2} a = 1$

To find the value of,

• $\frac{ 2 + 3 { \cos }^{2} a}{1 - 2 { \sin }^{2} a}$

Further solving,

We get,

$= > { \sin }^{2} a = \frac{1}{4}$

Now,

We know that,

• ${ \cos }^{2} \alpha = 1 - { \sin}^{2} \alpha$

Therefore,

We get,

$= > { \cos }^{2}a = 1 - \frac{1}{4} = \frac{4 - 1}{4} \\ \\ = > { \cos }^{2} a = \frac{3}{4}$

Therefore,

Putting the respective values,

We get,

$= > \frac{2 + 3 { \cos }^{2}a }{1 - 2 { \sin}^{2}a } \\ \\ = \frac{2 + (3 \times \frac{3}{4} )}{1 -( 2 \times \frac{1}{4} )} \\ \\ = \frac{2 + \frac{9}{4} }{1 - \frac{1}{2} } \\ \\ = \frac{ \frac{8 + 9}{4} }{ \frac{2 - 1}{2} } \\ \\ = \frac{ \frac{17}{4} }{ \frac{1}{2} } \\ \\ = \large \bold{ \frac{17}{2} }$