Question

求(sin105°-根号3倍cos105°)(根号3倍15°-sin15°)的值

Answer 1

(sin105°-√3cos105°)(√3cos15°-sin15°)
=2(1/2sin105º-√3/2cos105º)*2(√3/2*cos15º-1/2sin15º)
=4(sin105ºcos60º-cos105ºsin60º)(sin60ºcos15º-cos60ºsin15º)
=4sin(105º-45º)sin(60º-15º)
=4sin60ºsin45º
=4×√3/2×√2/2
=√6

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Answer 2

(sin105°-根号3倍cos105°)(根号3倍15°-sin15°)
=2(1/2sin105-根号3/2cos105)* 2(根号3/2cos15-1/2sin15)
=2(sin30sin105-cos30cos105)* 2(cos30cos15-sin30sin15)
=4(-cos(135))*(cos(45))
=4cos45cos45
=2(cos90+1)
=2