Question #7218e Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Apr 16, 2016 See below Explanation: LHS=left hand side, RHS =right hand side LHS=sin(2x+x)1+2cos2x =sin2xcosx+cos2xsinx1+2cos2x =(2sinxcosx)cosx+(1−2sin2x)sinx1+2cos2x =2sinxcos2x+sinx−2sin3x1+2(1−2sin2x) =2sinx(1−sin2x)+sinx−2sin3x1+2−4sin2x =2sinx−2sin3x+sinx−2sin3x3−4sin2x =3sinx−4sin3x3−4sin2x =sinx(3−4sin2x)3−4sin2x =sinx =RHS 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 1998 views around the world You can reuse this answer Creative Commons License