Is cot(2b)=(cot^2(b)-1)/(2cot(b)) ?

The answer to whether cot(2b)=(cot^2(b)-1)/(2cot(b)) is True

Popular >

prove cot(2b)=(cot^2(b)-1)/(2cot(b))

prove

cot (2 b) = \frac{cot ^{2} ( b ) - 1}{2 cot ( b )}

True

Solution steps

cot (2 b) = \frac{cot ^{2} ( b ) - 1}{2 cot ( b )}

Manipulating right side

\frac{cot ^{2} ( b ) - 1}{2 cot ( b )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ( 2 b )}{sin ( 2 b )}

Use the basic trigonometric identity:

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

= cot (2 b)

We showed that the two sides could take the same form

\Rightarrow True

1 + tan^{2} (a) = sec^{2} (a)

2 cos (x) cos (y) = cos (x + y) + cos (x - y)

\frac{1}{sec ^{2} ( θ )} + \frac{1}{csc ^{2} ( θ )} = 1

\frac{1}{cos ( - 1 )} - \frac{1}{cos ( + 1 )} = - 2 csc^{2} (x)

cos (x + π) cos (x - π) = cos^{2} (x)

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