Is cot(2θ)=cot(θ)-1/2 sec(θ)csc(θ) ?

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

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prove cot(2θ)=cot(θ)-1/2 sec(θ)csc(θ)

prove

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

True

Solution steps

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

Manipulating right side

cot (θ) - \frac{1}{2} sec (θ) csc (θ)

Express with sin, cos

= \frac{- 1 + 2 cos ^{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

(csc (x) - cot (x)) (csc (x) + cot (x)) = 1

(tan (x)) (sin (x)) = sec (x) - cos (x)

tan (α) + cot (α) = sec (α) csc (α)

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

cot (x) tan (x) = 1

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