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`2sin^(2)pi/6 +"cosec"(7pi)/(6)cos^(2)pi/3=3/2`

Answer» L.H.S. `2sin^(2)pi/2+"cosec"^(2)(7pi)/(6)cos^(2)pi/3`
`=2(sinpi/6)^(2)+["cosec"(7pi)/(6)cospi/3]^(2)`
`=2(sinpi/6)^(2)+["cosec"(pi+pi/6)cospi/3]^(2)`
`=2(sin180^(@))/(6))^(2) + ["cosec"(180^(@)+180^(@)/6)cos180^(@)/3]^(2)`
`=2(sin 30^(@))^(2) + [-"cosec"30^(@)cos60^(@)]^(2)`
`=2(1/2)^(2) + [-2 xx 1/2]^(2)`
`=1/2 +1=3/2`= RHS Hence proved.


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