Question

For all values of α for which the expression is defined, tan(2α)cos2α=

Answer 1

The expression tan(2α)cos2α is defined for all values of α that are not odd multiples of π/2.

Step-by-step explanation:

To find all values of α for which the expression tan(2α)cos2α is defined, we need to consider the domains of the trigonometric functions involved.

First, we know that tan(2α) is defined for all values of α that are not odd multiples of π/2. This means that α cannot be equal to (2n + 1)π/4, where n is an integer.

Second, cos2α is defined for all values of α. Therefore, the expression tan(2α)cos2α is defined for all values of α that are not odd multiples of π/2.

Answer 2

The expression tan(2α)cos2α involves applying trigonometric identities such as the double angle identity for tangent and the Pythagorean identity to simplify the expression and potentially cancel terms.

Step-by-step explanation:

The student is asking for a clarification on a trigonometric expression involving the function tan(2α)cos2α. To proceed with the calculation, we need to apply trigonometric identities to simplify the expression. According to the double angle identity for tangent, tan(2α) = 2tanα / (1 - tan2α), and from the Pythagorean identity, we know that cos2α = 1 - sin2α. To express cos2α in terms of tanα, we can use the identity tanα = sinα / cosα. Substituting cos2α expressed in terms of tanα into the original expression will allow for further simplification and cancellation of terms if possible.