Is 2cos(x)sec^2(x)= 2/(cos(x)) ?

The answer to whether 2cos(x)sec^2(x)= 2/(cos(x)) is True

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prove 2cos(x)sec^2(x)= 2/(cos(x))

prove

2 cos (x) sec^{2} (x) = \frac{2}{cos ( x )}

True

Solution steps

2 cos (x) sec^{2} (x) = \frac{2}{cos ( x )}

Manipulating left side

2 cos (x) sec^{2} (x)

Express with sin, cos

2 cos (x) sec^{2} (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Apply rule

1^{a} = 1

1^{2} = 1

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

Cancel the common factor:

cos (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{( sin ( t ) + cos ( t ) ) ^{2}}{sin ( t ) cos ( t )} = 2 + sec^{2} (t) (csc^{2} (t))

sec (x) + cos (x) = 1 + cos^{2} (x)

(cot (x) + tan (x)) sin (x) = sec (x)

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

csc (x) - cos (x) tan (x) = csc (x) - sin (x)

Is 2cos(x)sec^2(x)= 2/(cos(x)) ?
The answer to whether 2cos(x)sec^2(x)= 2/(cos(x)) is True