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if cos a = ¾, then the value of 16 cos^2(a/2) – 32 sin(a/2) sin (5a/2) is

if cos a = ¾, then the value of 16 cos^2(a/2) – 32 sin(a/2) sin (5a/2) is

Grade:11

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hello student, Please find the answer to your question below

use cos a = 1 – 2 sin^a/2
Form here find sin a/2
now 6 cos^2(a/2) – 32 sin(a/2) sin (5a/2)
= 6 [1 – sin^a/2 ] – 32 sin(a/2) sin (5a/2)

Now put the value of sin a/2 in above
Sakshi
11 Points
6 years ago
32sinA/2.sin5A/2 
use formula ,

2sinA.sinB = cos(A -B) -cos(A+B) 
cos2A = 2cos²A -1
cos3A = 4cos³A -3cosA 


now, 
32sinA/2.sin5A/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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