Is tan(z)*cos(z)*csc(z)=1 ?

The answer to whether tan(z)*cos(z)*csc(z)=1 is True

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prove tan(z)cos(z)csc(z)=1

prove

tan (z) \cdot cos (z) \cdot csc (z) = 1

True

Solution steps

tan (z) cos (z) csc (z) = 1

Manipulating left side

tan (z) cos (z) csc (z)

Express with sin, cos

cos (z) csc (z) tan (z)

Use the basic trigonometric identity:

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

= cos (z) \frac{1}{sin ( z )} tan (z)

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (z)

= \frac{1 \cdot cos ( z )}{cos ( z )}

Cancel the common factor:

cos (z)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

tan (π - θ) = - tan (x)

cot (θ) (sin (θ) + tan (θ)) = cos (θ) + 1

(2 - sin^{2} (x)) csc^{2} (x) = cot^{2} (x)

\frac{1}{tan ( A )} + tan (A) = \frac{2}{sin ( 2 A )}

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

Is tan(z)*cos(z)*csc(z)=1 ?
The answer to whether tan(z)*cos(z)*csc(z)=1 is True