求值sin5°×sin55°×sin65°
2个回答
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sin5°sin55°sin65°
=sin5°(cos10°-cos120°)/2
=(sin5°cos10°+1/2sin5°)/2
=(cos85°cos10°+1/2sin5°)/2
=[(cos95°+cos75°)/2+1/2sin5°]/2
=[(-sin5°+sin15°)/2+1/2sin5°]/2
=1/4sin15°
=1/4sin(45°-30°)
=1/4(sin45°cos30°-cos45°sin30°)
=1/4(√2/2·√3/2-√2/2·1/2)
=(√6-√2)/8。
=sin5°(cos10°-cos120°)/2
=(sin5°cos10°+1/2sin5°)/2
=(cos85°cos10°+1/2sin5°)/2
=[(cos95°+cos75°)/2+1/2sin5°]/2
=[(-sin5°+sin15°)/2+1/2sin5°]/2
=1/4sin15°
=1/4sin(45°-30°)
=1/4(sin45°cos30°-cos45°sin30°)
=1/4(√2/2·√3/2-√2/2·1/2)
=(√6-√2)/8。
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sin5°sin55°sin65°
=sin5°(cos10°-cos120°)/2
=(sin5°cos10°+1/2sin5°)/2
=(cos85°cos10°+1/2sin5°)/2
=[(cos95°+cos75°)/2+1/2sin5°]/2
=[(-sin5°+sin15°)/2+1/2sin5°]/2
=1/4sin15°
=1/4sin(45°-30°)
=1/4(sin45°cos30°-cos45°sin30°)
=1/4(√2/2·√3/2-√2/2·1/2)
=(√6-√2)/8。
=sin5°(cos10°-cos120°)/2
=(sin5°cos10°+1/2sin5°)/2
=(cos85°cos10°+1/2sin5°)/2
=[(cos95°+cos75°)/2+1/2sin5°]/2
=[(-sin5°+sin15°)/2+1/2sin5°]/2
=1/4sin15°
=1/4sin(45°-30°)
=1/4(sin45°cos30°-cos45°sin30°)
=1/4(√2/2·√3/2-√2/2·1/2)
=(√6-√2)/8。
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