Is cot(x)sec(x)= 1/(sin(x)) ?

The answer to whether cot(x)sec(x)= 1/(sin(x)) is True

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prove cot(x)sec(x)= 1/(sin(x))

prove

cot (x) sec (x) = \frac{1}{sin ( x )}

True

Solution steps

cot (x) sec (x) = \frac{1}{sin ( x )}

Manipulating left side

cot (x) sec (x)

Express with sin, cos

cot (x) sec (x)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

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

Use the basic trigonometric identity:

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

= \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

Simplify

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} : \frac{1}{sin ( x )}

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

Multiply fractions:

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

= \frac{cos ( x ) \cdot 1}{sin ( x ) cos ( x )}

Cancel the common factor:

cos (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{6 tan ( x ) + 6 cot ( y )}{tan ( x ) cot ( y )} = 6 tan (y) + 6 cot (x)

tan^{2} (x) sin^{2} (x) = tan^{2} (x) + sin^{2} (x)

cos (- \frac{π}{6}) = sin (- \frac{π}{6} + \frac{π}{2})

3 sin (2 x - 15) = cos (2 x - 15)

cos^{2} (x) - 2 sin^{2} (x) = 3 cos^{2} (x) - 2

Is cot(x)sec(x)= 1/(sin(x)) ?
The answer to whether cot(x)sec(x)= 1/(sin(x)) is True