By using the trigonometric identities, the expression that is equivalent is d. 2cos(α) - sec α
How to find equivalent expression
To find the expression equivalent to sec α cos (2α), use trigonometric identities.
Recall the double angle identity for cosine: cos (2α) = 2
(α) - 1.
Substituting this in the expression sec α cos (2α):
sec α cos (2α) = sec α * (2
(α) - 1)
Use the identity sec α = 1 / cos α:
sec α cos (2α) = (1 / cos α) * (2
(α) - 1)
Distribute the 1 / cos α:
sec α cos (2α) = 2
(α) / cos α - 1 / cos α
Simplify:
sec α cos (2α) = 2cos(α) - sec α
Therefore, the correct option is:
d. 2cos(α) - sec α