2(√6+√2)[sinA+sin(150-A)]得4(√6+√2)*sin75cos(A-75)

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2(√6+√2)[sinA+sin(150-A)]得4(√6+√2)*sin75cos(A-75)2(√6+√2)[sinA+sin(150-A)]得4(√6+√2)*sin75cos(A-75)2(

2(√6+√2)[sinA+sin(150-A)]得4(√6+√2)*sin75cos(A-75)
2(√6+√2)[sinA+sin(150-A)]

4(√6+√2)*sin75cos(A-75)

2(√6+√2)[sinA+sin(150-A)]得4(√6+√2)*sin75cos(A-75)
sinA+sinB=2sin[(A+B)/2]cos[(A-B)/2]

sinA+sin(150-A)
=2sin75*cos(75-A)
=2sin(30+45)*cos(A-75)
=2[sin30cos45+cos30sin45]*cos(A-75)
=2[√2/4+√6/4]*cos(A-75)
=(√2+√6)/2*cos(A-75)
所以:2(√6+√2)·[sinA+sin(150-A)]
=2(√6+√2)(√2+√6)/2*cos(A-75)
=(√2+√6)^2*cos(A-75)
=(8+4√3)cos(A-75)

【参考答案】

2(√6+√2)[sinA+sin(150-A)]
=2(√6+√2)×2sin75°cos(A-75°)
=4(√6+√2)×(1/4)(√6+√2)cos(A-75°)
=(8+4√3)cos(A-75°)

积差化和公式

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