Question

How do you verify `(sin z + cos z) (tan z + cot z) = sec z + csc z`?

Answer 1

`tan z + cot z = sin z/cos z + cos z/sin z = (sin^2z + cos^2z)/(sin z cos z)=1/(sin z cos z)`. On the left of given equation, it reduces to (1/cos z +1/sin z)= sec z + csc z, as required..

Explanation:

`sin^2z + cos^2z = 1`