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Simplify the expression cos x/cot^2 x tan x csc x

Show all your steps in simplifying the expression

well, tan x csc x = sinx/cosx * 1/sinx = 1/cosx

so that gives us
cos x/cot^2 x * 1/cosx = 1/cot^2x = tan^2x

Did you know?

Did you know that you can simplify the expression cos x/cot^2 x tan x csc x by applying trigonometric identities? Here are the steps involved: 1. Start by breaking down each trigonometric function using their reciprocal identities: - cos x = 1/sin x - cot x = 1/tan x = cos x/sin x - tan x = sin x/cos x - csc x = 1/sin x 2. Substitute these values back into the main expression: cos x/cot^2 x tan x csc x = (1/sin x) / ((cos x/sin x)^2) * (sin x/cos x) * (1/sin x) 3. Simplify each term: - (1/sin x) / ((cos x/sin x)^2) = (1/sin x) * (sin x^2/cos^2 x) = sin x / cos^2 x 4. Continue simplifying: - (sin x / cos^2 x) * (sin x/cos x) * (1/sin x) = (sin^2 x / cos^3 x) * (1/sin x) = sin x / cos^3 x So, by following these steps, the expression cos x/cot^2 x tan x csc x simplifies to sin x / cos^3 x.