Is cot(2θ)= 1/2 (cot(θ)-tan(θ)) ?

The answer to whether cot(2θ)= 1/2 (cot(θ)-tan(θ)) is True

Popular >

prove cot(2θ)= 1/2 (cot(θ)-tan(θ))

prove

cot (2 θ) = \frac{1}{2} (cot (θ) - tan (θ))

True

Solution steps

cot (2 θ) = \frac{1}{2} (cot (θ) - tan (θ))

Manipulating right side

\frac{1}{2} (cot (θ) - tan (θ))

Express with sin, cos

= \frac{cos ^{2} ( θ ) - sin ^{2} ( θ )}{2 cos ( θ ) sin ( θ )}

Rewrite using trig identities

= \frac{cos ( 2 θ )}{sin ( 2 θ )}

Use the basic trigonometric identity:

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

= cot (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

- cot (t) + \frac{sin ( t )}{1 - cos ( t )} = csc (t)

\frac{1}{1 - sin ( r )} = sec^{2} (r) + sec (r) tan (r)

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

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

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

Is cot(2θ)= 1/2 (cot(θ)-tan(θ)) ?
The answer to whether cot(2θ)= 1/2 (cot(θ)-tan(θ)) is True