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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

1 + sin (4 a) + sin (2 a) = sin (2 a)

cot (x) sec (x) = \frac{1}{sin ( x )}

\frac{6 tan ( x ) + 6 cot ( y )}{tan ( x ) cot ( y )} = 6 tan (y) + 6 cot (x)

tan^{2} (x) sin^{2} (x) = tan^{2} (x) + sin^{2} (x)

cos (- \frac{π}{6}) = sin (- \frac{π}{6} + \frac{π}{2})

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