Answer to Question #52550 in Trigonometry for tifg

Question

What is the actual value of arc sin(12/13) +arc sin(4/5)+arc sin(1). show the process using arc sinx +arc sin y formula?


using formula for the first two it comes pi - arc sin (56/65) then + arc sin 1 which is pi/2 . so the final result is 3pi/2 - arc sin (56/65) . and if i dont write pi/2 instead of arc sin 1 , then the result is pi - arc sin (56/65) +arc sin 1 = pi + arc sin (33/65) using formula for arc sin 1 - arc sin (56/65). i m lil bit confused which one is correct ? is there any use of principal value

the calculator shows its approximately 210 degree , means its a third quadrent angle .

normally we know arc sinx +arc sin y = arc sin [x*sqrt(1-y^2) +y*sqrt(1-x^2)]. but if we use this , the answer comes arc sin (56/65) + pi/2 , which does not match with the calculator result . so is there any regulation for arc sinx +arc sin y formula and is it applicable for (arc sinx +arc sin y) < pi/2 ?????