Question

Evaluate sin² 27° + sin² 87° + sin² 33

Answer 1

sin²27 + {sin²87 + sin²33}

= sin²27 + ( sin87 + sin33 )² -2sin87.sin33

[ use, formula,
sinA + sinB = 2sin(A + B)/2 .cos(A - B)/2
2sinA.sinB =cos(A - B) - cos(A + B) ]

=sin²27 + ( 2sin(87+33)/2.cos(87-33)/2 )² -{ cos(87-33) - cos(87 + 33) }

= sin²27 + (2×√3/2 cos27)² -cos54 + cos120
= sin²27 + 3cos²27 + cos120 - cos54°

=(sin²27 + cos²27) +2cos²27 +cos120 -cos54

= 1 + 2cos²27 -1/2 -cos54°

= 1 - cos54° + 2cos²27° -1/2

[use, (1 - cosx ) =2sin²27]

= 2sin²27 +2cos²27 -1/2

=2 -1/2 = 3/2

Answer 2

Answer:

sin²27 + {sin²87 + sin²33} = sin²27 + ( sin87 + sin33 )² -2sin87.sin33 [ use, formula, sinA + sinB = 2sin(A + B)/2 .cos(A - B)/2 2sinA.