Considering only the values of α and β for which secαsecβcos(α−β) is defined, which of the following expressions is equivalent to secαsecβcos(α−β)?

Question

Select the correct answer below:

cotβ−cotα

1+tanαtanβ

tanα−tanβ

sin(α+β)/1−tanαtanβ

Answer 1

secαsecβcos(α - β) = (1/cosα)(1/cosβ)[cosαcosβ + sinαsinβ)

= 1 + (sinα/cosα)(sinβ/cosβ) = 1 + tanαtanβ