Is sec^3(x)= 1/(cos^3(x)) ?

The answer to whether sec^3(x)= 1/(cos^3(x)) is True

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prove sec^3(x)= 1/(cos^3(x))

prove

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

True

Solution steps

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

Manipulating left side

sec^{3} (x)

Express with sin, cos

sec^{3} (x)

Use the basic trigonometric identity:

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

= (\frac{1}{cos ( x )})^{3}

Simplify

(\frac{1}{cos ( x )})^{3} : \frac{1}{cos ^{3} ( x )}

(\frac{1}{cos ( x )})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{3}}{cos ^{3} ( x )}

Apply rule

1^{a} = 1

1^{3} = 1

= \frac{1}{cos ^{3} ( x )}

= \frac{1}{cos ^{3} ( x )}

= \frac{1}{cos ^{3} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = \frac{5}{13}

sec (x) - tan (x) \cdot sin (x) = \frac{1}{sec ( x )}

sin^{4} (x) + cos^{4} (x) = 1 - \frac{1}{2} sin^{2} (2 x)

\frac{( 1 + cos ( 2 y ) )}{sin ^{2} ( y )} = 2 cot^{2} (y)

- tan (t) - \frac{cos ( t )}{sin ( t ) - 1} = sec (t)

Is sec^3(x)= 1/(cos^3(x)) ?
The answer to whether sec^3(x)= 1/(cos^3(x)) is True