Prove that #(sin2x-cos2x)/(sinxcosx)=-cot2x#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Shwetank Mauria Mar 20, 2017 #(sin^2x-cos^2x)/(sinx cosx)=-cot2x# Explanation: I presume you mean #(sin^2x-cos^2x)/(sinx cosx)# and this can be written as #-(cos^2x-sin^2x)/(2sinx cosx)xx2# = #-(cos2x)/(sin2x)xx2# = #-2cot2x# 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 3137 views around the world You can reuse this answer Creative Commons License