How do you verify the identity #sqrt((1+sintheta)/(1-sintheta))=(1+sintheta)/abscostheta#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Jan 17, 2017 see below Explanation: Left Hand Side: #sqrt ((1+sin theta)/(1-sin theta))=sqrt ((1+sin theta)/(1-sin theta) *((1+sin theta)/(1+sin theta))# #=sqrt ((1+sin theta)^2/(1-sin ^2theta))# #=sqrt ((1+sin theta)^2/(cos ^2theta))# #=sqrt ((1+sin theta)^2) / sqrt (cos^2 theta)# #=(1+sin theta)/abs( cos theta)# since #sqrt(x^2) = abs(x)# #:.=# Right Hand Side Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove #\csc \theta \times \tan \theta = \sec \theta#? How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#? How do you show that #2 \sin x \cos x = \sin 2x#? is true for #(5pi)/6#? How do you prove that #sec xcot x = csc x#? How do you prove that #cos 2x(1 + tan 2x) = 1#? How do you prove that #(2sinx)/[secx(cos4x-sin4x)]=tan2x#? How do you verify the identity: #-cotx =(sin3x+sinx)/(cos3x-cosx)#? How do you prove that #(tanx+cosx)/(1+sinx)=secx#? How do you prove the identity #(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)#? See all questions in Proving Identities Impact of this question 7199 views around the world You can reuse this answer Creative Commons License