Question #b314f Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Anjali G Mar 30, 2017 #1/(sinxcosx)-tanx=cotx# Explanation: #1/(sinxcosx)-tanx# #=1/(sinxcosx)-sinx/cosx# #=1/(sinxcosx)-sinx/cosxcolor(red)(*sinx/sinx)# #=frac{1-sin^2x}{sinxcosx}# (Pythagorean identity in the numerator) #=frac{cos^2x}{sinxcosx}# #=frac{cosx}{sinx}# #=cotx# 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 1469 views around the world You can reuse this answer Creative Commons License