To simplify the given expression, we can start by using the trigonometric identity:
1 - cos^2(α) = sin^2(α)
Next, we can rewrite the expression as:
(1 - cos^2(α))(1 + tan^2(α))
Substitute sin^2(α) for 1 - cos^2(α):
(sin^2(α))(1 + tan^2(α))
Now, recall that tan(α) = sin(α) / cos(α), so tan^2(α) = sin^2(α) / cos^2(α)
Therefore, our expression becomes:
sin^2(α)(1 + sin^2(α) / cos^2(α))
Now, expand the expression:
sin^2(α) + sin^4(α) / cos^2(α)
Our simplified expression is:
To simplify the given expression, we can start by using the trigonometric identity:
1 - cos^2(α) = sin^2(α)
Next, we can rewrite the expression as:
(1 - cos^2(α))(1 + tan^2(α))
Substitute sin^2(α) for 1 - cos^2(α):
(sin^2(α))(1 + tan^2(α))
Now, recall that tan(α) = sin(α) / cos(α), so tan^2(α) = sin^2(α) / cos^2(α)
Therefore, our expression becomes:
sin^2(α)(1 + sin^2(α) / cos^2(α))
Now, expand the expression:
sin^2(α) + sin^4(α) / cos^2(α)
Our simplified expression is:
sin^2(α) + sin^4(α) / cos^2(α)