The value of (sin 300°.tan 330°.sec 420°)/(tan 135°.sin 210°.sec 315°) is?

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Answer 1 · 2018-07-07T12:14:01

#color(cyan)(=> sqrt2#

I quadrant - All +, II quadrant - sin, csc +, III quadrant - tan, cot +, IV quadrant - cos, sec +

#sin 300^@ = sin (360 - 300) = -sin 60 = -sqrt3/2#

#tan 330^@ = tan (360-330) = -tan 30 = -1/sqrt3#

#sec 420^@ = sec (360 + 60) = sec 60 = 2#

#tan 135^@ = tan(180-135) = -tan 45 = -1#

#sin 210^@ = sin(180 + 30) = -sin 30 = -1/2#

#sec 315^@ = sec (360 - 315) = sec 45 = sqrt2#

#(sin 300 * tan 330 * sec 420) / (tan 135 * sin 210 * sec 315)#

#=> (-sqrt3/2 * -1/sqrt3 * 2) / (-1 * -1/2 * sqrt2)#

#=> (sqrt3 * 2 * 2) / (2 * sqrt3 * sqrt2)#

#=> sqrt2#