How do I simplify sec x/tan x ? Trigonometry Right Triangles Relating Trigonometric Functions 2 Answers Sahar Mulla ❤ Feb 20, 2018 #sec x/tan x# #(1/cosx )/(sinx/cosx)# #1/cancelcosx xx cancelcosx/sinx# #1/sinx = cscx# VNVDVI · Stefan V. Feb 20, 2018 Answer: #csc(x)# Explanation: Recall that #tan(x)=sin(x)/cos(x)# Rewrite your expression: #sec(x)/[sin(x)/cos(x)]# Recall that #sec(x)=1/cos(x)# Rewrite again: #(1/cos(x))/(sin(x)/cos(x)]# #cos(x)# cancels out: #1/sin(x)=csc(x)# 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 2437 views around the world You can reuse this answer Creative Commons License