Given sec s = 5/3, where sin s < 0, and cot t = 1, where 0 < t < 𝜋/2, find sin(s − t) and cos(s + t).

Answer 1

Sec is inverse of cos. So cos is 3/5. Since sin is meg this is 4th quad angle. It is a 3,4,5 right triangle in quad IV.

sin s is -4/5

cot is inverse of tan so tan t is also 1. This is a 1,1, sq root 2 right triangle in quad I. The cos and sin of t are both 1/root 2

Then apply formulas

sin(s-t) = (sin s) (cos t) - (cos s) (sin t) =

-4/5 root 2. - 3/ 5 root 2 = 1/5 root 2. If you rationalize denominator it becomes root 2 / 10

cos(s+t) = (cos s)(cos t) - (sin s) (sin t) = 7/5 root 2

or 7root 2/10