Question

prove that question please

Answer 1

It's Pretty simple, 

We know that Cos(2A) = Cos²A - Sin²A, If you don't know it, Please do remember it,

Now, We also knew that , Tan A = Sin A / Cos A,

Inputting this value in above formula, We get,
$\frac{1- \frac{ Sin^{2} A }{ Cos^{2} A } }{1 + \frac{ Sin^{2} A }{ Cos^{2} A } }$,

and by solving this again we will get,

$\frac{Cos ^2 A- Sin^2 A}{Cos^2A + Sin^2 A}$,


We know that Cos² + Sin²A = 1,

=> We will finally get Cos² A - Sin² A,

As I told you above, Cos² A - Sin² A = Cos 2A,

Now we have proved this,

Hope you understand What I have done, Have a great day !

Thank you !