a Using algebra and trig identities show that secx tan x si

a. Using algebra and trig identities, show that sec(x) – tan (x) sin (x) = cos (x)

b. Using algebra and trig identities, show that (sin⁴ x – cos⁴ x)/ (sin² x – cos² x) = 1   

Solution

a. sec x - tanx sinx=cos x

Starting with the left side

sec x - tan x sin x

(1/cos x ) - (sin²x/cos x)= (1-sin²x)/cos x= cos²x/cos x=cos x

b. (sin⁴x - cos⁴x)/(sin²x-cos²x)= 1

Starting with the left side

(sin⁴x-cos⁴x)/(sin²x-cos²x)= (sin²x+cos²x)(sin²x-cos²x)/(sin²x-cos²x) = sin²x+ cos²x=1