Question

Exact value using sum and difference, Sin75°

Answer 1

Answer:

Step-by-step explanation:

   sin(75)=1+√32√2

Explanation:

sin(75)=sin(45+30)

The sine sum identity is:

sin(A+B)=sinAcosB+cosAsinB

∴ sin(75)=sin(45)cos(30)+cos(45)sin(30)

sin(75)=√22⋅√32+√22⋅12=√24(√3+1)

sin(75)=1+√32√2

Answer 2

Answer:

sin(75°) = $\frac{\sqrt{2}+\sqrt{6} }{4}$

Step-by-step explanation:

Given: sin(75°)

Rewrite: sin(30° + 45°)

Use sum and difference identity:

sin(α + β) = sinαcosβ + cosαsinβ

sin(30°+45°) = sin(30°)cos(45°) + cos(30°)sin(45°)

sin(30°+45°) = (1/2)(√2 / 2) + (√3 / 2)(√2 / 2)

sin(30°+45°) = (√2 / 4) + (√6 / 4)

sin(30°+45°) = [(√2 + √6) / 4]

sin(75°) = [(√2 + √6) / 4]