Is tan(μ)sec(μ)cos(μ)=tan(μ) ?

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

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prove tan(μ)sec(μ)cos(μ)=tan(μ)

prove

tan (μ) sec (μ) cos (μ) = tan (μ)

True

Solution steps

tan (μ) sec (μ) cos (μ) = tan (μ)

Manipulating left side

tan (μ) sec (μ) cos (μ)

Rewrite using trig identities

tan (μ) sec (μ) cos (μ)

sec (μ) cos (μ) = 1

sec (μ) cos (μ)

Express with sin, cos

sec (μ) cos (μ)

Use the basic trigonometric identity:

sec (μ) = \frac{1}{cos ( μ )}

= \frac{1}{cos ( μ )} cos (μ)

\frac{1}{cos ( μ )} cos (μ) = 1

\frac{1}{cos ( μ )} cos (μ)

Multiply fractions:

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

= \frac{1 cos ( μ )}{cos ( μ )}

Cancel the common factor:

cos (μ)

= 1

= 1

= tan (μ) \cdot 1

Simplify

= tan (μ)

= tan (μ)

We showed that the two sides could take the same form

\Rightarrow True

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