How do you simplify secx(cosx+sinx)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Alan P. Feb 25, 2016 sec(x)(cos(x)+sin(x))=1+tan(x) Explanation: sec(x)=1cos(x) Therefore sec(x)(cos(x)+sin(x)) XXX=1cos(x)⋅cos(x)+1cos(x)⋅sin(x) XXX=1+sin(x)cos(x) XXX=1+tan(x) Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove cscθ×tanθ=secθ? How do you prove (1−cos2x)(1+cot2x)=1? How do you show that 2sinxcosx=sin2x? is true for 5π6? How do you prove that secxcotx=cscx? How do you prove that cos2x(1+tan2x)=1? How do you prove that 2sinxsecx(cos4x−sin4x)=tan2x? How do you verify the identity: −cotx=sin3x+sinxcos3x−cosx? How do you prove that tanx+cosx1+sinx=secx? How do you prove the identity sinx−cosxsinx+cosx=2sin2x−11+2sinxcosx? See all questions in Proving Identities Impact of this question 4693 views around the world You can reuse this answer Creative Commons License