Question

If cos A =1/2
find the value of
2 sec A/1+tan² A
​

Answer 1

Step-by-step explanation:

$\frac{2 \sec( \alpha ) }{1 + { \tan}^{2} \alpha } \\ = \frac{ \frac{2}{ \cos( \alpha ) } }{1 + \frac{ { \sin}^{2} \alpha }{ { \cos }^{2} \alpha } } \\ = \frac{ \frac{2}{ \cos( \alpha ) } }{ \frac{ { \cos }^{2} \alpha + { \sin}^{2} \alpha }{ { \cos}^{2} \alpha } } \\ = \frac{ \frac{2}{ \cos( \alpha ) } }{ \frac{1}{ { \cos }^{2} \alpha } } \\ = \frac{2}{ \cos( \alpha ) } \times { \cos }^{2} \alpha \\ = 2 \cos( \alpha ) \\ = 2 \times \frac{1}{2} = 1$