Question

Write the trig expression in terms of sine and cosine then simplify.
1. cos t tan t
2. cos t csc t

Answer 1

Hello,

1) cos t* tan t=cos t* sin t/cos t =sin t (if cos t≠0)

2)cos t * cosec t =cos t /sin t =√(1-sin² t) / sin t.

Answer 2

when we multiply cos t and tan t, the result is cos2 x over sin x. cos2 x is equal to 1 - sin2 x. the simplified form is 1/sin x  - sin x. csc t is the inverse of sin t. hence the cos t over sin t is equal to cot t. The answer in two is cos t over sin t