How do you find a numerical value of one trigonometric function of x given #tanx=1/4secx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Nov 12, 2016 #x=0.2526802551+2pin or x=2.888912398+2pin# Explanation: #tanx=1/4 secx# #sinx/cosx=1/4 *1/cosx# #sinx/cosx*cosx=1/4*1/cosx*cosx# #sinx/cancelcosx*cancelcosx=1/4*1/cancelcosx*cancelcosx# #sinx=1/4# #x=sin^-1(1/4)# #x=0.2526802551+2pin or x=(pi-0.2526802551)+2pin# #x=0.2526802551+2pin or x=2.888912398+2pin# 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 2072 views around the world You can reuse this answer Creative Commons License