Is (1-cos(b))(1+cos(b))= 1/(csc^2(b)) ?

The answer to whether (1-cos(b))(1+cos(b))= 1/(csc^2(b)) is True

Popular >

prove (1-cos(b))(1+cos(b))= 1/(csc^2(b))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{csc ^{2} ( b )}

Express with sin, cos

= sin^{2} (b)

Rewrite using trig identities

= (1 + cos (b)) (1 - cos (b))

= (1 - cos (b)) (1 + cos (b))

We showed that the two sides could take the same form

\Rightarrow True

sin (θ - \frac{π}{2}) = cos (π + θ)

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

\frac{cos ( x )}{sin ( x ) + 1} = sec (x) - tan (x)

tan (- 7) = tan (π - 7)

sin (x) - 1 = cos (x)

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