Verify the identity 1/ 1 − sin x − 1/ 1 + sin x = 2 sec x tan x

Answer 1

lets work on the left side 1/1-sin - 1/1+sin

combine into one fraction

common denominator is (1-sin)(1+sin) which is 1-sin^2

this will give us

(1+sin)-(1-sin)/1-sin^2

but 1-sin^2= cos^2 which gives us

2sin/cos^2

on the right side substitute 1/cos for secant and sin/cos for tan

which gives us 2(1/cos)(sin/cos)=2sin/cos^2