how do you prove the identity that log(1-sinx)+log(1+sinx)=2log(cosx)

Answer 1

log(1-sinx)+log(1+sinx)=2log(cosx)

Recall that addition is multiplication so

log(1-sinx)+log(1+sinx)=

log[(1-sinx)(1+sinx)]

Foil (1-sinx)(1+sinx)=1-sin²x=cos²x

Plug back in

log(cos²x)

log(cos)²

Move the exponent to the front to finish the proof

2log(cosx)