Write cos t in terms of tan t where t terminates in quadrant

Write cos t in terms of tan t, where t terminates in quadrant IV

Solution

We use the trigonometry identity sec² t – tan² t = 1 to find sec t in terms of tan t

sec t = ± (1 + tan² t)

Since t is in quadrant IV where sec (t) is positive, Hence

sec t = (1 + tan² t)

We now calculate cos (t) as follows

cos t = 1 / sec t

so, cos t = 1 / (1 + tan² t)