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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

tan (x) sec (x) cos (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

= tan (x) \cdot 1

Simplify

= tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (2 y) = \frac{1 - tan ^{2} ( y )}{1 + tan ^{2} ( y )}

sin (θ) cot^{2} (θ) = cos^{2} (θ) csc (θ)

\frac{sec ( x ) tan ( x )}{sec ^{2} ( x )} = sin (x)

sin (α) = \frac{1}{csc ( α )}

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