Simplify csc x - cos x cot x
1/sin x - cos^2 x/sin x
(1-cos^2 x)/sin x
sin^2 x/sin x
sin x
csc x - cos x cot x
=1/sinx - cosx(cos/sin)
= (1 - cos^2x)/sinx
= sin^2 x/sinx
= sinx
To simplify the expression csc x - cos x cot x, we'll use the trigonometric identities to rewrite the terms in a simpler form.
First, let's rewrite the expression using the reciprocal identities:
csc x = 1/sin x
cot x = 1/tan x
Now we can substitute these values back into the expression:
csc x - cos x cot x = 1/sin x - cos x * (1/tan x)
Next, let's simplify the expression further by combining the fractions:
1/sin x - cos x * (1/tan x) = (1 - cos x)/sin x - cos x/sin x
Now we have a common denominator, so we can combine the terms:
(1 - cos x)/sin x - cos x/sin x = (1 - cos x - cos x)/sin x
Simplifying further, we have:
(1 - cos x - cos x)/sin x = (1 - 2cos x)/sin x
Therefore, the simplified form of csc x - cos x cot x is (1 - 2cos x)/sin x.