implify and write the trigonometric expression in terms of sine and cosine: sec(t)-cos(t) divided by sec(t)=f(t)^2.

Question

Please write in terms of sine and cosine!

Answer 1

(f(t))² = (sect - cost)/sect

 

          = (1/cost - cost) / (1/cost)

 

          = [ (1 - cos²t)/cost ] (cost)

 

          = sin²t

 

So, f(t) = ±sint

 

 

Answer 2

(sect-cost)/sect=F(t)^2

sect/sect-cost/sect=F(t)^2

1-cost/sect=F(t)^2

sec=1/cos

cost/sect=cost*cost=cos^2t

1-cos^2t=F(t)^2

1-cos^2t=sin^2t

sin^2t=F(t)^2

√sin^2t=√F(t)^2

F(t)=sint

Answer 3

f(t)² = [sec t - cos t]/sec t

       = [(1/cos t) - cos t]/(1/cos t)

       = [(1 - cos² t)/cos t]/(1/cos t)

       = 1 - cos² t                                 [cos t ≠ 0; t ≠ (2k+1)90°]

       = sin² t

 

f(t) = ± sin t.  More information about t is needed to know if f(t) =  sin t or f(t) = - sin t.