Prove the identities sec^2 ? csc^2 ? = sec^2 + csc^2 ?

Question

These confuse me so much 

Answer 1

Let ? = x

 

 

We know the basic identities:

 

sec²(x) = 1 / cos²(x)

 

csc²(x) = 1 / sin²(x)

 

 

We want the left side to equal the right side of equation.  If we multiply the left side out, we end up with

 

1 / cos²(x)sin²(x).

 

 

We need the right side to equal this term. 

 

(1 / cos²(x)) + (1 / sin²(x)) =

 

(sin²(x) + cos²(x)) / cos²(x)sin²(x) =

 

1 / cos²(x)sin²(x)

 

 

The right side equals the left side.  The identity is proven.