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sin A + 2 sin 2 A + sin 3 Ais equal to which of the following ? 1.4sin2Acos^(2)((A)/(2)) 2.2 sin2A("sin"(A)/(2)+"cos"(A)/(2))^(2)3.8sin A cos A cos ^(2)((A)/(2))Select the correct answer using the code given below : |
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Answer» 1 and 2 only `rArrsinA+2sin2A=sin3A=sin30^(@)+2sin60^(@)+sin90^(@)` `=(1)/(2)+(2sqrt(3))/(2)+1=(2sqrt(3)+3)/(2)` `(because2cos^(2)A=1+cos2A)` Now , `4sin2Acos^(2)((A)/(2))=2sin2A[1+cosA]` `=2sin60^(@)[1+COS30^(@)]=(2sqrt(3)+3)/(2)` Also ,`sin2A=2sinAcosA&SIN^(2)A+cos^(2)A=1` `2sin2A["sin"(A)/(2)+"cos"(A)/(2)]^(2)` `=2sin2A["sin"^(2)(A)/(2)"cos"^(2)(A)/(2)+2"sin"(A)/(2)"cos"(A)/(2)]` `=2sin2A[1+sinA]=2sin60^(@)[1+sin30^(@)]` `=(3sqrt(3))/(2)` & 8 sin A cos A`cos^(2)((A)/(2))` `=4sinAcosA[1+cosA]` `=4sin30^(@)cos30^(@)[1+cos30^(@)]` `=(2sqrt(3)+3)/(2)` |
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