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Grade: 11

                        

What is the Minimum value of cos 2 (60+x) - cos 2 (60-x) is

2 years ago

Answers : (2)

Saurabh Koranglekar
askIITians Faculty
8407 Points
							576-1048_1.PNG
						
2 years ago
Sripad Sambrani
19 Points
							
cos^2(60+x)-cos^2(60-x)
= [(1+cos(120+2x))-(1+cos(120-2x))]/2; since cos^2x=[1+cos2x]/2
= [cos(120+2x)-cos(120-2x)]/2
= [-2*sin120*sin2x]/2; since cos(A+B)-cos(A-B)=-2sinA*sinB
= -sin120*sin2x = -(√3/2)*sin2x
 
range(sinA)=(-1,1)
Hence range(-(√3/2)*sin2x)=(-√3/2, √3/2)
Minimum value of given expression is -√3/2
 
Trust this helps
one year ago
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