Question

1/secA+tanA = 1-sinA/cosA

Answer 1

Below.

Explanation:

1 / secA+tanA = 1 / [1/cosA+sinA/cosA))]

= 1/ [(1 + sinA)/cosA]

= cosA/(1+sinA)

Now check if this is identical to 1-sinA/cosA:

1-sinA/cosA = cosA/(1+sinA)

Cross multiply:

(1-sinA)(1+sinA) = cos^2A

1 - sin^2A = cos^2A

sin^2A + cos^2A = 1

This is a known idenity.

So the original identity is true.