Question #50ca2 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Andrea S. Mar 27, 2017 cosθ1−sinθ=secθ+tanθ Explanation: Start from the first member: cosθ1−sinθ multiply and divide by (1+sinθ): cosθ1−sinθ=cosθ1−sinθ1+sinθ1+sinθ cosθ1−sinθ=cosθ1+sinθ1−sin2θ cosθ1−sinθ=cosθ1+sinθcos2θ cosθ1−sinθ=1+sinθcosθ cosθ1−sinθ=1cosθ+sinθcosθ cosθ1−sinθ=secθ+tanθ 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 1395 views around the world You can reuse this answer Creative Commons License