explain this step This indeterminate form may be resolved by multiplying by $1=$ conjugate

conjugate where conjugate is

the conjugate of the denominator. A basic trigonometric identity is also required.

lim

x$0$

$3$ sin$2$ x

$1$ cos x $=$ lim

x$0$

$3$ sin$2$ x

$1$ cos x $1+$ cos x

$1+$ cos x $=$ lim

x$0$

$3$ sin$2$ x$(1+$ cos x$)$

$(1+$ cos x$)(1$ cos x$)$

$=$ lim

x$0$

$3$ sin$2$ x$(1+$ cos x$)$

$1$ cos$2$ x

$=$ lim

x$0$

$3$ sin$2$ x$(1+$ cos x$)$

sin$2$ x

$=$ lim

x$03(1+$ cos x$)=3(1+$ cos $0)=3(1+1)=6$