Is cot(θ)= 1/(\frac{sin(θ)){cos(θ)}} ?

The answer to whether cot(θ)= 1/(\frac{sin(θ)){cos(θ)}} is True

Popular >

prove cot(θ)= 1/(\frac{sin(θ)){cos(θ)}}

prove

cot (θ) = \frac{1}{\frac{s i n ( θ )}{c o s ( θ )}}

True

Solution steps

cot (θ) = \frac{1}{\frac{s i n ( θ )}{c o s ( θ )}}

Manipulating right side

\frac{1}{\frac{s i n ( θ )}{c o s ( θ )}}

Simplify

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

1 = 1 + cot (θ)

\frac{sin ^{2} ( A )}{csc ^{2} ( A )} = sin^{4} (A)

1 - tan^{4} (θ) = 2 sec^{2} (θ) - sec^{4} (θ)

Is cot(θ)= 1/(\frac{sin(θ)){cos(θ)}} ?
The answer to whether cot(θ)= 1/(\frac{sin(θ)){cos(θ)}} is True