Write the trig expression in terms of sine and cosine then simplify.

1. cos t tan t

2. cos t csc t

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.

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