Is (cos(x))(tan(x))(csc(x))=1 ?

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

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

prove

(cos (x)) (tan (x)) (csc (x)) = 1

True

Solution steps

cos (x) tan (x) csc (x) = 1

Manipulating left side

cos (x) tan (x) csc (x)

Express with sin, cos

cos (x) csc (x) tan (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

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

Cancel the common factor:

cos (x)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( x ) tan ( x )}{1 + tan ( x )} = cos (x)

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

1 - 2 sin^{4} (x) = 1 - 2 sin^{2} (x)

sin (z + w) = sin (z) cos (w) + cos (z) sin (w)

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

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