Is tan(x+pi/2)=-cot(x) ?

The answer to whether tan(x+pi/2)=-cot(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove tan(x+pi/2)=-cot(x)

prove

tan (x + \frac{π}{2}) = - cot (x)

True

Solution steps

tan (x + \frac{π}{2}) = - cot (x)

Manipulating left side

tan (x + \frac{π}{2})

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= - cot (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (θ) tan (θ) csc (θ) = 1

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

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

\frac{cos ( π - x )}{cos ( \frac{π}{2} + x )} = cot (x)

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