verify identity

Question

sin(X)sec(x)=1-(cos^2)x/sin(X)cos(X)

Answer 1

You need the following two identities for this problem:

 

sec(x) = 1/cos(x)

sin²x + cos²x = 1

 

Now let's use them in your problem:

 

sin(x)sec(x) = [1-cos²(x)]/sin(x)cos(x)

 

sin(x)/cos(x) = sin²(x)/sin(x)cos(x)       [sec(x) = 1/cos(x), 1-cos²(x)=sin²(x)]

 

sin(x)/cos(x) = sin(x)/cos(x)

 

QED