Is tan(θ)cot(θ)=1 ?

The answer to whether tan(θ)cot(θ)=1 is True

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prove tan(θ)cot(θ)=1

prove

tan (θ) cot (θ) = 1

True

Solution steps

tan (θ) cot (θ) = 1

Manipulating left side

tan (θ) cot (θ)

Express with sin, cos

cot (θ) tan (θ)

Use the basic trigonometric identity:

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

= \frac{cos ( θ )}{sin ( θ )} tan (θ)

Use the basic trigonometric identity:

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

= \frac{cos ( θ )}{sin ( θ )} \cdot \frac{sin ( θ )}{cos ( θ )}

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

\frac{cos ( θ )}{sin ( θ )} \cdot \frac{sin ( θ )}{cos ( θ )}

Multiply fractions:

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

= \frac{cos ( θ ) sin ( θ )}{sin ( θ ) cos ( θ )}

Cancel the common factor:

cos (θ)

= \frac{sin ( θ )}{sin ( θ )}

Cancel the common factor:

sin (θ)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{2} - x) = sin (x)

sin (\frac{π}{2} - θ) = cos (θ)

cot^{2} (x) + 1 = csc^{2} (x)

sec (u) - tan (u) = \frac{cos ( u )}{1 + sin ( u )}

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