How do you simplify #((sin x) ^3 - (cos x) ^3)/(tan x)^3#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N. Nov 27, 2015 Simplify trig expression Explanation: #(sin^3 x - cos^3 x)/(tan^3 x) = (sin^3 x)/tan^3 x - (cos^3 x)/tan^3 x =# #= cos^3 x - (cos^3 x.cos^3 x)/(sin^3 x) = cos^3 x(1 - cot^3 x)# Answer link Related questions What does it mean to find the sign of a trigonometric function and how do you find it? What are the reciprocal identities of trigonometric functions? What are the quotient identities for a trigonometric functions? What are the cofunction identities and reflection properties for trigonometric functions? What is the pythagorean identity? If #sec theta = 4#, how do you use the reciprocal identity to find #cos theta#? How do you find the domain and range of sine, cosine, and tangent? What quadrant does #cot 325^@# lie in and what is the sign? How do you use use quotient identities to explain why the tangent and cotangent function have... How do you show that #1+tan^2 theta = sec ^2 theta#? See all questions in Relating Trigonometric Functions Impact of this question 3054 views around the world You can reuse this answer Creative Commons License