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