Differentiate \sqrt{\frac{1+\sin x}{1-\sin x}}

Turnseeuw

Turnseeuw

Answered question

2022-01-23

Differentiate 1+sinx1sinx

Answer & Explanation

spelkw

spelkw

Beginner2022-01-24Added 12 answers

By the half-angle formulae we obtain
1+sinx1sinx=1cos(x+π2)1+cos(x+π2)=tan(x2π4)
Maritza Mccall

Maritza Mccall

Beginner2022-01-25Added 17 answers

Logarithmic differentiation makes things easier
y=1+sinx1sinxlog(y)=12log(1+sin(x))log(1sin(x))
yy=12cosx1+sinx+cosx1sinx
Simplify as much as you can and, when finished, use
y=y×yy

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