Question

Prove (cscx+cotx)(cscx-cotx)=1

((1/sinx)+(cos/sinx))(1/sinx-(cosx/sinx))

(1+cosx/sinx)(1-cosx/sinx)

I don't understand what to do next or if I even Have it right

Answer 1

my immediate reaction from the beginning would have been "difference of squares! csc^2 x - cot^2 x = 1"
i cant remember any identities about those functions tho

Answer 2

i guess if you use 1= sin^2 x / sin^2 x, you can multiply everything by sin^2 x and get
1 - cos^2 x = sin^2 x

which can be manipulated to a known identity

Answer 3

You can use the idea that cos^2(x) + sin^2(x) = 1. Then divide all terms by sin^2(x) to get


cos^2(x)/sin^2(x) + sin^2(x)/sin^2(x) = 1/sin^2(x)

cot^2(x) + 1 = csc^2(x)

1 = csc^2(x) - cot^2(x)

csc^2(x) - cot^2(x) = 1


So csc^2(x) - cot^2(x) = 1 is an identity

Answer 4

Thank You :))

Answer 5

you're welcome