What is e^{(-ln(sin(x))+C)} ?

The solution to e^{(-ln(sin(x))+C)} is e^Ccsc(x)

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simplify e^{(-ln(sin(x))+C)}

simplify

e^{(- l n (s i n (x)) + C)}

e^{C} csc (x)

Solution steps

e^{- l n (s i n (x)) + C}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{- l n (s i n (x))} e^{C}

Simplify

e^{- l n (s i n (x))} : sin^{- 1} (x)

= sin^{- 1} (x) e^{C}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

sin^{- 1} (x) = \frac{1}{sin ( x )}

= e^{C} \frac{1}{sin ( x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot e ^{C}}{sin ( x )}

Multiply:

1 \cdot e^{C} = e^{C}

= \frac{e ^{C}}{sin ( x )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= e^{C} csc (x)

2 sec (2) (8 ϕ) - 1

- 6 π cos (120 π t + \frac{π}{2})

sin (x + nπ)

sin (+ arcsin (t))

sin (\frac{π}{2} + 2 π x)