Is (cot(x))(sec(x))(sin(x))=1 ?

The answer to whether (cot(x))(sec(x))(sin(x))=1 is True

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prove (cot(x))(sec(x))(sin(x))=1

prove

(cot (x)) (sec (x)) (sin (x)) = 1

True

Solution steps

cot (x) sec (x) sin (x) = 1

Manipulating left side

cot (x) sec (x) sin (x)

Express with sin, cos

cot (x) sec (x) sin (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

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

Cancel the common factor:

sin (x)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{cos ( a )}{1 - sin ( a )} - tan (a) = sec (a)

p ro v e tan (\frac{θ}{2}) + cot (\frac{θ}{2}) = 2 csc (θ)

p ro v e sin^{2} (2 θ) = 4 sin^{2} (θ) cos^{2} (θ)

p ro v e \frac{cos ( 4 x ) + cos ( 6 x )}{sin ( 4 x ) - sin ( 6 x )} = - cot (x)

p ro v e 2 sin^{2} (x) = (1 - cos (2 x))

Is (cot(x))(sec(x))(sin(x))=1 ?
The answer to whether (cot(x))(sec(x))(sin(x))=1 is True