Question

find the value of sin 105 + cos 105

Answer 1

Answer:

The answer of the above question is 1/√2.

Step-by-step explanation:

Sin(60°+45°) +Cos(60°+45°)

={(Sin60°Cos45°+Cos60°Sin45°)+(Cos60°Cos45°-Sin60°Sin45°)}

=[{(√3/2)(1/√2)+(1/2)(1/√2)}+{(1/2)(1/√2)-(√3/2)(1/√2)}]

=[(√3/2√2)+(1/2√2)]+[(1/2√2)-(√3/2√2)]

=((√3+1)/2√2)+((1-√3)/2√2)

=(√3+1+1-√3)/2√2

=(2/2√2)

=1/√2 (Answer)

Hope it helps