Question

Verify the identity:
ln|1+cscθ|+ln|1−cosθ|=2ln|sinθ|

Answer 1

holy sh*t...

Answer 2

\[\ln{|(1-\cos \theta)(1+ \cos \theta) |} = 2\ln|\sin \theta|\]

\[\ln|1-\cos^2 \theta| = \ln|\sin^2 \theta|\]

1-cos^2 x = sin^2 x

Therefore:

\[\ln|\sin^2 \theta| = \ln|\sin^2 \theta|\]

LHS = RHS.

Answer 3

where did the ln|(1−cosθ)(1+cosθ)| come from?

Answer 4

ln a + ln b = ln(ab)

Logarithm laws

Answer 5

aw. Thank you c: