Sum & Difference Formulas

Question

Find sin105° without using a calculator.

Answer 1

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

sin 105 = sin (60+45)

Plugging into the formula:

sin 60 cos 45 + cos 60 sin 45

(√3/2)(√2/2) + (1/2)(√2/2) simplify

(√6/4)+(√2/4) Simplify

(√6+√2)/4