# CBSE Class 11-science Answered

**cos^2 5@+ cos^2 10@+cos^2 15@...........+cos^2 180@**

Asked by vermahiteshi243 | 30 Aug, 2021, 09:53: AM

Expert Answer

Let α = cos

^{2}5 + cos^{2}10 + cos^{2}15 + cos^{2}25 + .............................+ cos^{2}1802α - 36 = ( 2cos

^{2}5 - 1 ) + (2 cos^{2}10 - 1 ) + .............................+ (2cos^{2}180-1)2α - 36 = cos10 + cos20 + cos30 +....................................+ cos360

2α - 36 = ( cos10 + cos360 ) + ( cos20 +.cos350 ) ..................+ (cos180 + cos190)

2α - 36 = ( 2 cos185 cos 175 ) + ( 2 cos185 cos165 ) + ..................+ ( 2 cos185 cos5 )

2α - 36 = 2 cos185 [ cos175 + cos165 + cos 155 + ........................+ cos15 + cos 5 ]

2α - 36 = 2 cos185 [ ( cos175 + cos 5 ) + ( cos165 + cos15) ..................... + ( cos95 + cos85) ]

2α - 36 = 2 cos185 [ ( 2 cos90 cos85 ) + ( 2 cos90 cos75 ) + .................... + ( 2 cos90 cos 5) ]

2α - 36 = 4 cos185 cos90 [ cos85 + cos75 + .....................+ cos 5 ]

In above expression , in RHS , we get cos90 . Hence we have , 2α - 36 = 0 or α = 18

Hence we get , α = cos

^{2}5 + cos^{2}10 + cos^{2}15 + cos^{2}25 + .............................+ cos^{2}180 = 18
Answered by Thiyagarajan K | 17 Sep, 2021, 12:27: PM

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