y = sec t tan t = 1/ cos t * sin t / cos t = sin t / cos² t
[tex]y`= \frac{cos t cos ^{2} t-2 cost*(-sin t)*sint}{cos^{4} t}= \\ =\frac{cos ^{3} t+2costsin^{2}t }{cos ^{4}t }= \\ = \frac{cos ^{2} t+2sin ^{2} t}{cos ^{3} t}= \\ = \frac{1-sin ^{2}t+2sin ^{2} t }{cos ^{3}t }= \\ = \frac{1+sin ^{2} t}{cos ^{3}t } [/tex]
