Sin330cos120+cos210sin300=??

1 Answer
sankarankalyanam
Mar 7, 2018

#=> color(brown)(1)#

Explanation:

#sin 330 cos 120 + cos 210 sin 300#

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#=> (sin (360 - 30) * cos (180 - 120)) + (cos (180+ 30) * sin (360 - 60)#

From the diagram, sin is negative in IV quadrant & cos negative in II & III quadrants.

#=> ((-sin 30) * (-cos 60)) + ((-cos30) * (-sin 60))#

#=> (sin 30 * cos 60) + (cos 30 * sin 60)#

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#=> ((1/2) * (1/2)) + ((sqrt3/2) * (sqrt3/2))#

#=> 1 / 4 + 3 / 4 = 1#

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