if cosecA=root3, find the value of 2 sin2A +3cot2A
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cosecA=_/3
so, sin A=1/_/3
cos A=_/(1-sin^2 A)=_/(2/3)
2sin 2A + 3cot 2A
=>2*2sinAcosA + 3(cos 2A/sin 2A)
=>4sinAcosA+3((cos^2 A - sin^2A)/sin2A
=>4*1/_/3*_/(2/3)+3((2/3-1/3)/2*1/_/3*_/(2/3
=>(4_/2)/3 + 3(1/3)/(_/2)/3
=>(4_/2)/3 + 3/_/2
=>(4_/2)/3 + (3_/2)/2
=>((2*4_/2) + (3*3_/2))/6
=>(8_/2 + 9_/2)/6
=>(17_/2)/6
so, sin A=1/_/3
cos A=_/(1-sin^2 A)=_/(2/3)
2sin 2A + 3cot 2A
=>2*2sinAcosA + 3(cos 2A/sin 2A)
=>4sinAcosA+3((cos^2 A - sin^2A)/sin2A
=>4*1/_/3*_/(2/3)+3((2/3-1/3)/2*1/_/3*_/(2/3
=>(4_/2)/3 + 3(1/3)/(_/2)/3
=>(4_/2)/3 + 3/_/2
=>(4_/2)/3 + (3_/2)/2
=>((2*4_/2) + (3*3_/2))/6
=>(8_/2 + 9_/2)/6
=>(17_/2)/6
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