If sin theta/2 = 1/2 (a+ 1/a ), prove that: cos theta = - 1/2 * (a ^ 2 +1/a^2)

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

step-by-step explanation:

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed