if cosA=2/3,then find the value of 32sin(A/2) sin(5A/2)
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Answer:
32sinA/2.sin5A/2
use formula ,
2sinA.sinB = cos(A -B) -cos(A+B)
cos2A = 2cos²A -1
cos3A = 4cos³A -3cosA
now,
32sinA/2sin5A/2 = 16cos2A -16cos3A
16{ 2cos²A -1 -4cos³A+3cosA}
=16{ 2(3/4)²-1-4(3/4)³+3(3/4)}
=16{ 18/16 -1 -27/16 +36/16}
=( 18 -16 -27 +36}
=11
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