Trigonometry-5

From Homeworkwiki

Show that cos A (tan A + 2) (2 tan A + 1) = 2 sec A + 5 sin A

Solution: L.H.S. = cos A (2 tan² A + 5 tan A + 2)

= cos A [ (2 (tan² A + 1) + 5 Tan A]

= cos A (2 sec² A + 5 tan A) = cos A [2/cos² A + 5 sin A / cos A]

= [2 / cos A + 5 sin A] = 2 sec A + 5 sin A = R. H. S.