Is cot(θ)-2cot(2θ)=tan(θ) ?

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

Popular >

prove cot(θ)-2cot(2θ)=tan(θ)

prove

cot (θ) - 2 cot (2 θ) = tan (θ)

True

Solution steps

cot (θ) - 2 cot (2 θ) = tan (θ)

Manipulating left side

cot (θ) - 2 cot (2 θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan (3 π + θ) = tan (θ)

4 sin (- x) cos (- x) = - 2 sin (2 x)

(4 sin (θ) + 4 cos (θ))^{2} = 16 + 16 sin (2 θ)

1 - sin (θ) = cos^{2} (θ)

\frac{1}{sec ( a ) - tan ( a )} = sec (a) + tan (a)

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