What is e^{ln(1/(cos(x)))+c} ?

The solution to e^{ln(1/(cos(x)))+c} is e^csec(x)

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simplify e^{ln(1/(cos(x)))+c}

simplify

e^{l n (\frac{1}{c o s ( x )}) + c}

e^{c} sec (x)

Solution steps

e^{l n (\frac{1}{c o s ( x )}) + c}

Apply exponent rule:

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

= e^{l n (\frac{1}{c o s ( x )})} e^{c}

Simplify

e^{l n (\frac{1}{c o s ( x )})} : \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} e^{c}

Multiply fractions:

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

= \frac{1 \cdot e ^{c}}{cos ( x )}

Multiply:

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

= \frac{e ^{c}}{cos ( x )}

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= e^{c} sec (x)

sin (\frac{π}{4} + \frac{x}{2})

tan (arccos (\frac{x}{7}))

sinh (\frac{1}{cosh ( l )})

cos (arctan (\frac{u}{4}))

\frac{6 sin ( - 0.1 )}{x}

What is e^{ln(1/(cos(x)))+c} ?
The solution to e^{ln(1/(cos(x)))+c} is e^csec(x)