(1-cosA)(1+cosA)(1+cos^2A)

asked by guest
on Sep 19, 2024 at 6:00 pm



You asked:

Evaluate the expression: \(\left(1 - \cos\left( A \right)\right) \cdot \left(1 + \cos\left( A \right)\right) \cdot \left(1 + {\cos\left( A \right)}^{2}\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(1 - \cos\left( A \right)\right) \cdot \left(1 + \cos\left( A \right)\right) \cdot \left(1 + {\cos\left( A \right)}^{2}\right) = \left(1 - \cos{\left(A \right)}\right) \left(\cos{\left(A \right)} + 1\right) \left(\cos^{2}{\left(A \right)} + 1\right) \)

Expanded

\[\left(1 - \cos\left( A \right)\right) \cdot \left(1 + \cos\left( A \right)\right) \cdot \left(1 + {\cos\left( A \right)}^{2}\right) = 1 - \cos^{4}{\left(A \right)}\]

Factored

\[\left(1 - \cos\left( A \right)\right) \cdot \left(1 + \cos\left( A \right)\right) \cdot \left(1 + {\cos\left( A \right)}^{2}\right) = - \left(\cos{\left(A \right)} - 1\right) \left(\cos{\left(A \right)} + 1\right) \left(\cos^{2}{\left(A \right)} + 1\right)\]

+ Submit Question