Verify the given identity Simplify your answers completely 2

Verify the given identity. (Simplify your answers completely.) 2 tan (x)/1 + tam^2(x) = sin (2x) Show that the left hand side of the equation is equivalent to the right hand side. 2 tan(x)/1 + tan^1(x)

Solution

L.H.S = 2tan(x) / 1+tan^2 x

but tanx = sinx/cosx

= 2tanx / (1 +sin^2 x /cos^2x ) ----> Answer in 1st box

=2tanx /(sin^2 x +cos^2 x) /cos^2x

= 2tanx . cos^2x -------------> Answer in 2nd box

= 2 sinx/cosx. cos^2 x ----> Answer in third box

= 2sinx cosx ->4th box

= sin(2x)

L.H.S = R.H.S

so hence proved