Question

Evaluate lim x tends to zero cos2x-1/cosx-1​

Answer 1

hey......
.
.
The limit as x approaches 0 is 4. This can be shown as follows :

Using the trigonometric identity cos ( 2x ) = 2cos^2(x) - 1 , We get the following :

[ ( 2cos^2(x) - 1 ) - 1 ] / cos ( x ) - 1

Next , we can simplify :
( 2cos^2(x) - 2 ) / ( cos ( x ) - 1 ) = 2 ( cos^2(x) - 1 ) / ( cos ( x ) - 1 )

We are able to factor the numerator like so :

2 ( cos (x) + 1 ) ( cos (x) - 1 ) / ( cos (x) - 1 ) =
2 ( cos (x) + 1 )

Finally we can take the limits as X , approaches 0 by plugging 0 directly into the equation.

2 ( cos ( 0 ) + 1 ) = 2 ( 1 + 1 ) = 2 ( 2 ) = 4 .
.
.
.
.
.
.
.
i hope this helps u.
.
.
mark me brainliest plz plz