Step-by-step explanation:
[tex]cos2a=cos^2a-sin^2a[/tex]
Lets derive this equation,
we can write ,
[tex]cos2a= cos(a+a)[/tex]
going by the identity,
[tex]cos(a+b)= cosa cosb - sina sinb[/tex]
using the identity ,
[tex]cos(a+a)= cosacosa-sinasina[/tex] .................(1)
After simplification of equation no.1 we get -
[tex]cos(2a)=cos^2a-sin^2a[/tex] ............... (for any value of a)
Hence the equation is proved for every value of a.
