Question

using the half amgle formulas, find the exact value of
(i)sin15°
(ii)sin 585°/2

Answer 1

cosθ=1-2sin²θ/2

1-cosθ=2sin²θ/2

sinθ/2=√1-cosθ/2

=====================

sin15° = √[1-cos30/2 ]

√[1-(√3/2)/2 ]

√ 1/2 [ 1- √3/2 ]

√ 1/2 - √3/4

= √ 2- √3 / 4

= √(2-√3) /2

multiply by √2/√2

=√ (2-√3)2/2√2

=√4-2√3/2√2

=√(√3-1)² / 2√2

=√3-1/2√2

= √ 3 -1 /2√2

and

sin585/2= sin (90*6+45)/2

=sin45/2

=sin22.5

=√ 1- 1/√2 / 2

=√(√2-1/√2)/2

multiply by √2/√2

=√2-√2/√2²

= √ 2-√2/2

hope helped !