1 point Write each expression in terms of sines andor cosine

(1 point) Write each expression in terms of sines and/or cosines and then simplify. (cos(x) tan(x) + 1)(sin(x)-1) = (1-sin(x))(1 + sin(x)) = (1 + cos(x))(1 - cot(x) sin(x))-

Solution

( cos x tan x + 1 ) ( sin x -1 )

tan x = sin x / cos x

( cos x sin x / cos x +1 ) ( sin x -1 )

( sin x + 1 ) ( sin x -1 )

= sin^2 x -1

2) ( 1 - sin x ) ( 1 + sin x )

1 - sin x + sin x - sin^2 x

1 - sin^2 x

= cos^2 x

3) ( 1 + cos x ) ( 1 - cot x sin x )

cot x = cos x / sin x

( 1 + cos x ) ( 1 - cos x )

1 - cos^2 x

= sin^2 x