Write each expression in terms of sines and/or cosines and then simplify:

Question

1. sec (x) / tan(x) 

 

2. sin (x) / csc (x) + cos ^2 (x)

 

3. sin (x) / csc (x) - sec (x)cos (x)

Answer 1

Sec x = 1 ÷ cos x 

 

Sec x / tan x = 

 

1  / cos x * cos x / sin x

 

= 1 ÷ sin x

 

2) csc x = 1 / sin x 

 

So sin x / cscx 

 

= sin^2 X

 

Finally sin^2 X + cos^2 X =  1

 

3) sin^2 X -  1