Question

How do you prove `1/(sec D - tan D) + 1/(sec D + tan D) = 2 sec D`?

Answer 1

Prove : `1/(sec D - tan D) + 1/(sec D + tan D) = 2sec D`

Explanation:

Left side --> `((sec D + tan D) + (sec D - tan D))/(sec^2D - tan^2 D) =`
`= (2sec D)/1`
because:
`sec^2 D - tan^2 D = 1/(cos^2 D) - (sin^2 D)/(cos^2 D) =`
`= (1 - sin^2 D)/(cos ^2 D) = (cos^2 D)/(cos^2 D) = 1`