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 2242 views around the world You can reuse this answer Creative Commons License