varify the identity: csc^2(X) - (CosX)(SecX) = Cot^2(X)

Question

please show all steps

 

Answer 1

We know that csc^x-cot^2x = 1

cosx = 1/secx

Left hand side

= csc^2(x)-cos(x)sec(x)

= csc^2(x)-(1/sec(x))sec(x)

= csc^2(x)-1

= cot^2(x)

= Right hand side.