What is ln((cos(x)-sin(x+pi))^{-1}) ?

The solution to ln((cos(x)-sin(x+pi))^{-1}) is ln(1/(cos(x)+sin(x)))

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simplify ln((cos(x)-sin(x+pi))^{-1})

simplify

ln ((cos (x) - sin (x + π))^{- 1})

ln (\frac{1}{cos ( x ) + sin ( x )})

Solution steps

ln ((cos (x) - sin (x + π))^{- 1})

Rewrite using trig identities

= ln ((cos (x) - (- sin (x)))^{- 1})

Simplify

ln ((cos (x) - (- sin (x)))^{- 1}) : ln (\frac{1}{cos ( x ) + sin ( x )})

= ln (\frac{1}{cos ( x ) + sin ( x )})

sec (45 π + x) \cdot cot (24 π - x)

cos (108 0^{\circ} - θ)

3 sin (\frac{π}{2} - π t)

sin (- 1 x)

\frac{sin ( - x )}{tan ( - x )}

What is ln((cos(x)-sin(x+pi))^{-1}) ?
The solution to ln((cos(x)-sin(x+pi))^{-1}) is ln(1/(cos(x)+sin(x)))