Question

Verify each identity:
(secx-tanx)^2=(1-sinx)/(1+sinx)

Answer 1

(secx-tanx)^2 = { 1/cos(x) - sin(x)/cos(x) }^2 = { (1-sin(x)) }^2 / cos^2(x) =
{ (1-sin(x)) }^2 / { 1 - sin^2(x) } = { (1-sin(x)) }^2 / { (1 + sin(x)) * (1 -sin(x)) } =
{1-sin(x)}/{1+sin(x)}

Answer 2

ok :) i understand most of it except for the last part when you multiplied the bottom by (1-sinx)

Answer 3

a^2 - b^2 = (a+b) * (a-b)
1 - sin^2(x) = 1^2 - sin^2(x) = (1+sin(x)) * (1-sin(x))

Answer 4

how come you didn't multiply the top?

Answer 5

We are not multiplying the top and bottom with the same thing here. We are just factoring the denominator, { 1 - sin^2(x) }, as (1+sin(x)) * (1-sin(x)) using the identity:
a^2 - b^2 = (a+b) * (a-b).

Answer 6

ohhhhhh ok :)

Answer 7

thank you so much! :)

Answer 8

@alessandro96