Simplifying Using Trig Identities

Question

If tan^2(t)-sin^2(t)=sin^a(t)/cos^b(t), then

the positive power a= 

the positive power b= 

Answer 1

Simplify the left side so that it is only in terms of sine and cosine.

 

(sin²t / cos²t) - sin²t =

 

(sin²t - sin²tcos²t) / cos²t =

 

sin²t(1 - cos²t) / cos²t =

 

sin³t / cos²t

 

 

a = 3

b = 2