Question

find sin105°+cos105°

Answer 1

sin105 + cos105
= 0.96592582628 + (-0.2588190451)
= 0.965925826- 0.258819045
= 0.707106781

Answer 2

Answer:

1/√2

Step-by-step explanation:

cos(105°) + sin(105°) can be rewritten as:

cos(45° + 60°) + sin(45° + 60°)

now, use the addition identities for cos and sin:

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

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

plug in a=45° and b=60° to the identities:

cos(45°)cos(60°) - sin(45°)sin(60°) + sin(45°)cos(60°) + cos(45°)sin(60°)

solve using knowledge of 45–45–90 and 30–60–90 triangles:

(√2)/2 • 1/2 - (√2)/2 • (√3)/2 + (√2)/2 • 1/2 + (√2)/2 • (√3)/2

simplify:

(√2)/4 - (√6)/4 + (√2)/4 + (√6)/4

 

(√2)/4 + (√2)/4

2(√2)/4

(√2)/2

=1/√2