Prove that: (sin 300)(tan 330)(sec 420) / (cot 135)(cos 210)(cosec 315)=-2÷2.44
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Sin 300 = sin (360- 60) = - sin 60 = - √3 /2
tan 330 = tan (360 - 30) = - tan 30 = - 1/√3
sec 420 = sec(360+60) = sec 60 = 2
cot 135 = cot (90+45) = - tan 45 = -1
cos 210 = cos (180+30) = - cos 30 = - √3/2
cosec 315 = cosec(360 - 45) = - cosec 45 = - √2
So LHS= -√3/2 * -1/√3 * 2 / [ -1 * -√3/2 * - √2 ]
= √(2/3)
tan 330 = tan (360 - 30) = - tan 30 = - 1/√3
sec 420 = sec(360+60) = sec 60 = 2
cot 135 = cot (90+45) = - tan 45 = -1
cos 210 = cos (180+30) = - cos 30 = - √3/2
cosec 315 = cosec(360 - 45) = - cosec 45 = - √2
So LHS= -√3/2 * -1/√3 * 2 / [ -1 * -√3/2 * - √2 ]
= √(2/3)
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