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

1 Answer
Nghi N.
Nov 7, 2015

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

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