Question

clarify the basics?!.........

Answer 1

Answer:

Step-by-step explanation:

LHS = sin(2a) / (1 + cos(2a))  

2sin(a)cos(a) / (1 + 2cos^2(a) - 1)  

= 2sin(a)cos(a) / (2cos^2(a))  

= sin(a) / cos(a)  

= tan(a)  

= RHS  

QED

Answer 2

You have reached almost to the final step. By manipulating, you can write the final form as any of the following:

$\sin(a) = \pm \sqrt{ \frac{ { \sec}^{2} (a) - 1 }{ {sec}^{2} (a)} } \\ \\ 1. \: \sin(a) = \pm \: \frac{ \sqrt{ { \sec}^{2} (a) - 1 }}{ \sqrt{ {sec}^{2} (a)} } \\ \\ = \pm \: \frac{ \sqrt{ { \sec}^{2} (a) - 1 }}{ {sec} (a)} \\ \\ 2.\: \sin(a) = \pm \: \frac{ \sqrt{ { \sec}^{2} (a) - 1 }}{ {sec} (a)} \\ \\ = \pm \: \frac{ \sqrt{ { \sec}^{2} (a) - {1}^{2} }}{ {sec} (a)} \\ \\ = \pm \: \frac{ \sqrt{ {( \sec}(a) + 1)( \sec(a) - 1) }}{ {sec} (a)}$

Those are two possible forms.

You can take the square
root of denominator. But you cant remove the square root from numerator now as it can not be written as a perfect square. If you put a value of sec(a), then you can take the square root