# Find the maximum value of sin² (120+a) +sin² (120-a)....give ans with explanation

2
by andymukhrj
max is 3/2
yah..ur ans is ri8...but plz expln

2014-08-09T10:56:34+05:30

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Sin² (120+a)  + sin² (120-a)

1/2 {  1 - cos (240+2a)  }    +  1/2  { 1 - cos (240-2a)  }
1 - 1/2  [ cos (240 + 2a)  +  cos ( 240 - 2a)  ]
1 - 1/2  [  cos 240 cos 2a - sin 240 sin 2a + cos 240 cos 2a + sin 240 sin 2a ]
1 - cos 240 sin 2a
1 - 1/2 sin 2a                as        cos 240 = cos (360 - 240)
maximum value is obtained when sin 2a is minimun and  is 0 when a = 0.

so 1

As cos 240 is -1/2, Given value is 1 + 1/2 sin 2a. So Maximum value is 3/2
2014-08-09T12:05:59+05:30
Sin² (120+a)  + sin² (120-a)

1/2 {  1 - cos (240+2a)  }    +  1/2  { 1 - cos (240-2a)  }
1 - 1/2  [ cos (240 + 2a)  +  cos ( 240 - 2a)  ]
1 - 1/2  [  cos 240 cos 2a - sin 240 sin 2a + cos 240 cos 2a + sin 240 sin 2a ]
1 - cos 240 sin 2a
1 - 1/2 sin 2a                as        cos 240 = cos (360 - 240)
maximum value is obtained when sin 2a is minimun and  is 0 when a = 0.

so 1