Is cos(x)(sec(x)tan(x))=tan(x) ?

The answer to whether cos(x)(sec(x)tan(x))=tan(x) is True

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prove cos(x)(sec(x)tan(x))=tan(x)

prove

cos (x) (sec (x) tan (x)) = tan (x)

True

Solution steps

cos (x) sec (x) tan (x) = tan (x)

Manipulating left side

cos (x) sec (x) tan (x)

Rewrite using trig identities

cos (x) sec (x) tan (x)

sec (x) cos (x) = 1

sec (x) cos (x)

Express with sin, cos

sec (x) cos (x)

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= 1

= 1

= 1 \cdot tan (x)

Simplify

= tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cot^{2} (x) \cdot sec^{2} (x) = csc^{2} (x)

cot (\frac{1}{2} x) = \frac{sin ( x )}{1 - cos ( x )}

\frac{2}{cos ^{2} ( x )} - tan^{2} (x) = tan^{2} (x) + 2

cos (π - t) = - cos (t)

Is cos(x)(sec(x)tan(x))=tan(x) ?
The answer to whether cos(x)(sec(x)tan(x))=tan(x) is True