Question

Tan(theta+45)+tan(theta-45) identical to 2 tan2theta

Answer 1

• sin(theta+45)/cos(theta+45)+sin(theta-45)/con(theta-45)
• (sin(theta+45).cos(theta-45))+(cos(theta+45).sin(theta-45))/cos(theta+45).cos(theta-45)
• apply formula in numerator sin(A+B)=sinAcosB+cosAsinB
• then
• Sin(theta+45+theta-45)/cos(theta+45).cos(theta-45)
• sin(2theta)/cos(theta+45).cos(theta-45)
• now mulitiply by 2 in numerator and denominator
• then
• 2sin(2theta)/2cos(theta+45).cos(theta-45)
• apply formula in denominator 2cosAcosB=cos(A+B)+cos(A-B)
• then
• 2sin(2theta)/cos(2theta)
• 2tan(2teta)
• hence proved