(4sinxcosx-2sinxsecx)/2tanx

Question

Help simplify the expression and show the steps too!

Answer 1

It should really be sin(x) not sinx

After the 1st step I am going to leave out the x's, - Just for now

1-it is too hard to type formulas here  2-you can see what I do easier

(4 sin(x) cos(x) - 2 sin(x) sec(x))    remove the 1/2

                2tan(x)

 

= 2sin cos - sin sec     redistribute the tan
               tan

 

= 2 sin cos - sin sec
        tan          tan

You should remember tan = sin/cos 

this is Much more useful than tan = o/h

 

 = 2   sin cos -  sin sec
        sin / cos    sin / cos

= 2  sin cos - sin sec
       sin / cos  sin / cos

 

= 2   cos    -  sec cos     using sec = 1/cos (see below)

        1/cos                1/ 1/cos = cos   so  cos/ 1/cos = cos²

 

You should remember the 6 functions like this (its easier)

learn to think and write down the 6 functions

sin cos tan cotan sec cosec in this "U" shape

 

sin       cosec     = 1/sin    (so also sin = 1/cosec)

cos      sec         = 1/cos   (so also cos = 1sec    )

tan      cotan      = 1/tan   (so also tan = 1/cotan)

 

= 2 cos² -   1   cos     =  2 cos²(x) - 1

                 cos

 

There are many other ways to reduce it, here are just a few.

 

= 1/2 cot(x) (4 sin(x) cos(x)-2 tan(x))

or

= 1-2 sin²(x)

or

= cos(2 x)

 

If you want to learn easy ways to remember your trig,

Search the internet for - "Trig Without Tears"