Question #08381 Trigonometry Right Triangles Relating Trigonometric Functions 2 Answers Adam L. · Scott F. Mar 21, 2017 1 Explanation: Remember #cot(x) = cos(x)/sin(x)# #((cos^2(x)/sin^2(x))cos^2(x))/((cos^2(x)/sin^2(x))-cos^2(x))# #((cos^2(x)/sin^2(x))(cos^2(x)/1))/((cos^2(x)/sin^2(x))-((cos^2(x)sin^2(x))/sin^2(x))# #(cos^4(x)/sin^2(x))/((cos^2(x)-sin^2(x)cos^2(x))/sin^2(x))# #cos^4(x)/(cos^2(x)-sin^2(x)cos^2(x))# #cos^4(x)/(cos^2(x)(1-sin^2(x))# #cos^2(x)/(1-sin^2(x))# Use trig identities, specifically: #sin^2(x)+cos^2(x)=1# #cos^2(x)=1-sin^2(x)# #cos^2(x)/cos^2(x)# 1 Answer link P dilip_k Mar 27, 2017 #(cot^2xcos^2x)/(cot^2x-cos^2x)# #=((csc^2x-1)cos^2x)/(cot^2x-cos^2x)# #=((1/sin^2x-1)cos^2x)/(cot^2x-cos^2x)# #=(cos^2x/sin^2x-cos^2x)/(cot^2x-cos^2x)# #=(cot^2x-cos^2x)/(cot^2x-cos^2x)=1# 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 1852 views around the world You can reuse this answer Creative Commons License