Question

Cos a = 3/4 find 16cos²(a/2) - 32sin(a/2)sin(5a/2)

Answer 1

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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