Establish the Identity

[jgchickenman]

I need some help with this difficult problem.

Establish the identity (make one side look like the other)
1-sin(x)/cos(x)+cos(x)/1-sin(x)=2sec(x)

 

[Deleted member 4993]

I need some help with this difficult problem.

Establish the identity (make one side look like the other)
1-sin(x)/cos(x)+cos(x)/1-sin(x)=2sec(x)

First of all, use grouping symbols to indicate order of operation correctly.

The left-hand-side should be written as follows:

[1-sin(x)]/cos(x) + cos(x)/[1-sin(x)]

= [{1-sin(x)}² + cos²(x)]/[cos(x)*{1-sin(x)}]

simplify and continue.....

 

[jgchickenman]

First of all, use grouping symbols to indicate order of operation correctly.

The left-hand-side should be written as follows:

[1-sin(x)]/cos(x) + cos(x)/[1-sin(x)]

= [{1-sin(x)}² + cos²(x)]/[cos(x)*{1-sin(x)}]

simplify and continue.....

I got to this point where all I need to do is simplify and that is where I need help. Wasn't specific in original question, sorry.

 

[Deleted member 4993]

I got to this point where all I need to do is simplify and that is where I need help. Wasn't specific in original question, sorry.

Well - you do know

(a + b)² = a² + b² + 2ab

and

cos²(x) + sin²(x) = 1

Use those.....