Evaluate. Q.2. Using principal values, evaluate the following. cos - 1 cos 2 π 3 + sin - 1 sin 2 π 3 . Share with your friends Share 0 Neha Sethi answered this Dear student cos-1cos2π3+sin-1sin2π3Consider, cos-1cos2π3=cos-1-12If a=cos-1b⇒cosa=b for 0≤a≤πx=cos-1-12⇒cosx=-12, 0≤x≤πNow, cosx=-12 , 0≤x≤πGeneral solution for cosx=-12x=2π3+2nπ, x=4π3+2nπSolutions for the range 0≤x≤πx=2π3Consider, sin-1sin2π3=sin-132If a=sin-1b⇒sina=b for -π2≤a≤π2x=sin-132⇒sinx=32, -π2≤x≤π2General solution for sinx=32Now, sinx=32 ,-π2≤x≤π2x=π3+2nπ, x=2π3+2nπSolutions for the range -π2≤x≤π2x=π3So, cos-1cos2π3+sin-1sin2π3=2π3+π3=π Regards 0 View Full Answer Pritkumar answered this HOPE MIGHT BE USEFUL 0 N I S H I D H A . answered this I too got the same answer but in back its written as "pi" is the required answer. :/ Thats why I got confused. Is it possible that the back page answer is wrong? I think so. Thanks :D 0 Nisarg answered this cos^-1(cos(2π/3)) + sin^-1(sin(2π/3) = 2π/3 + sin^-1(sin(π-π/3)) (This is because principal value branch of cos^-1 lies in [0,π] while that of sin^-1 lies in [-π/2,π/2]) = 2π/3 + sin^-1(sin(π/3)) = 2π/3 + π/3 = 3π/3 = π P.S. It coincides with the answer at the back of your textbook! Sorry if the answer is not formatted. That's the fault of meritnation website. 2
