Cosine 35 degrees sine 55 degrees plus sine 35 degrees cosine 55 degreees?

This is the Trig. Identity .

Sin( A + B) = SinACosB + CosASinB.

Hence

Sin55Cos35 + Cos555Sin35 =

Sin(55 + 35) = Sin(90) = 1

Verification

If you take the various Sin & Cos values and multiply then add, they will answer to '1'.

Hence./

(0.819153..)(0.819152...) +(0.573576...)(0,573586...) =

0.67100999 + 0.328989 = 0.99995... ~ 1. as required.