Verify whether sin75square root6square root24SolutionWell wr

Verify whether sin75=(square root6+square root2)/4

Solution

We\'ll write 75 as a sum of 2 angles:

75 = 45 + 30

We\'ll apply sine function both sides:

sin(75) = sin(45+30)

We\'ll use the identity:

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

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

sin(45+30) = (sqrt2/2)*(sqrt3/2) + (1/2)*(sqrt2/2)

sin(45+30) = sqrt(2*3)/4 + sqrt2/4

sin(45+30) = (sqrt6 + sqrt2)/4

We notice that we get the indicated result, therefore the identity sin(75) = (sqrt6 + sqrt2)/4 is verified.