Is ((2sec(x)))/(tan(x))=2csc(x) ?

The answer to whether ((2sec(x)))/(tan(x))=2csc(x) is True

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prove ((2sec(x)))/(tan(x))=2csc(x)

prove

\frac{( 2 sec ( x ) )}{tan ( x )} = 2 csc (x)

True

Solution steps

\frac{2 sec ( x )}{tan ( x )} = 2 csc (x)

Manipulating left side

\frac{2 sec ( x )}{tan ( x )}

Express with sin, cos

\frac{2 sec ( x )}{tan ( x )}

Use the basic trigonometric identity:

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

= \frac{2 \cdot \frac{1}{c o s ( x )}}{tan ( x )}

Use the basic trigonometric identity:

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

= \frac{2 \cdot \frac{1}{c o s ( x )}}{\frac{s i n ( x )}{c o s ( x )}}

Simplify

\frac{2 \cdot \frac{1}{c o s ( x )}}{\frac{s i n ( x )}{c o s ( x )}} : \frac{2}{sin ( x )}

\frac{2 \cdot \frac{1}{c o s ( x )}}{\frac{s i n ( x )}{c o s ( x )}}

Apply the fraction rule:

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

= \frac{2 \cdot \frac{1}{c o s ( x )} cos ( x )}{sin ( x )}

Multiply

2 \cdot \frac{1}{cos ( x )} cos (x) : 2

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

Multiply fractions:

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

= \frac{1 \cdot 2 cos ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1 \cdot 2

Multiply the numbers:

1 \cdot 2 = 2

= 2

= \frac{2}{sin ( x )}

= \frac{2}{sin ( x )}

= \frac{2}{sin ( x )}

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{2}{\frac{1}{c s c ( x )}}

Simplify

\frac{2}{\frac{1}{c s c ( x )}}

Apply the fraction rule:

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

= \frac{2 csc ( x )}{1}

Apply rule

\frac{a}{1} = a

= 2 csc (x)

2 csc (x)

2 csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sec^{2} (y) = (sec (y))^{2}

csc (A) = \frac{7}{4}

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

csc (cos (+ sin (x))) = cot (+ 1)

Is ((2sec(x)))/(tan(x))=2csc(x) ?
The answer to whether ((2sec(x)))/(tan(x))=2csc(x) is True