How to show \(\displaystyle{\ln{{\left({\tan{{\left({x}\right)}}}+{\sec{{\left({x}\right)}}}\right)}}}={\frac{{{\ln{{\left({1}+{\sin{{x}}}\right)}}}-{\ln{{\left({1}-{\sin{{x}}}\right)}}}}}{{{2}}}}\) is true or false

Breanna Fisher

Breanna Fisher

Answered question

2022-04-09

How to show
ln(tan(x)+sec(x))=ln(1+sinx)ln(1sinx)2 is true or false

Answer & Explanation

abangan85s0

abangan85s0

Beginner2022-04-10Added 16 answers

We'll start from RHS
12[ln(1+sinx)ln(1sinx)]=12[ln(1+sinx1sinx)]
=12[ln((1+sinx)21sin2x)]
=12[ln((1+sinx)2cos2x)]
=ln(1+sinxcosx)
=ln(1cosx+sinxcosx)
=12[ln(1+sinx)ln(1sinx)]=ln(secx+tanx)
So it's true

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