




Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Examples
Example 2 Important
Example 3
Example 4
Example 5 Important
Example 6 Important
Example 7 Important
Example 8
Example 9 Important
Example 10
Example 11 Important
Example 12
Example 13
Example 14
Example 15
Example 16 Important
Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21 Important
Example 22 Important You are here
Question 1 Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Last updated at June 22, 2023 by Teachoo
Example 22 Prove that cos2 ๐ฅ+cos2 (๐ฅ+๐/3) + cos2 (๐ฅโ๐/3) = 3/2 Lets first calculate all 3 terms separately We know that cos 2x = 2 cos2 x โ 1 cos 2x + 1 = 2cos2 x ๐๐๐ โกใ2๐ฅ + 1ใ/2 = cos2 x cos2 x = ๐๐จ๐ฌโกใ๐๐ + ๐ใ/๐ Replacing x with ("x + " ๐ /๐) cos2 ("x" +๐ /๐) = cosโกใ2(๐ฅ + ๐/3)+1ใ/2 = ๐๐๐โกใ(๐๐ + ๐๐ /๐) + ๐ใ/๐ Similarly, Replacing x with ("x โ" ๐ /๐) in cos2 x = ๐๐จ๐ฌโกใ๐๐ + ๐ใ/๐ cos2 ("x" โ๐/3) = cosโกใ2(๐ฅ โ ๐/3)+ 1ใ/2 = cosโกใ(2๐ฅ โ 2๐/3)+ 1ใ/2 Solving L.H.S cos2 x + cos2 (๐ฅ+ ๐/3) + cos2 (๐ฅโ๐/3) = (๐ + ๐๐จ๐ฌโก๐๐)/๐ + (๐ + ๐๐๐โก(๐๐ + ๐๐ /๐))/๐ + (๐ + ๐๐๐โก(๐๐ โ ๐๐ /๐))/๐ = 1/2 [1+cosโกใ2๐ฅ+1+๐๐๐ (2๐ฅ+2๐/3)+1+๐๐๐ (2๐ฅโ2๐/3)ใ ] = 1/2 [3+cosโกใ2๐ฅ+๐๐๐(๐๐+๐๐ /๐)+๐๐๐(๐๐โ๐๐ /๐)ใ ] = 1/2 [3+cosโกใ2๐ฅ+2๐๐๐((๐๐ + ๐๐ /๐ + ๐๐ โ ๐๐ /๐)/๐).๐๐๐((๐๐ + ๐๐ /๐ โ(๐๐ โ ๐๐ /๐))/๐)ใ ] = 1/2 [3+cosโกใ2๐ฅ+2๐๐๐ ((4๐ฅ + 0)/2).๐๐๐ ((0 + 4๐/3)/2)ใ ] = 1/2 [3+cosโกใ2๐ฅ+2๐๐๐ (4๐ฅ/2).๐๐๐ ((4๐/3)/2)ใ ] = 1/2 [3+cosโกใ2๐ฅ+๐ ๐๐จ๐ฌโก๐๐ ๐๐จ๐ฌโกใ๐๐ /๐ใ ใ ] = 1/2 [3+cosโกใ2๐ฅ+2 cosโก2๐ฅ cosโก(๐โ๐/3) ใ ] = 1/2 [3+cosโกใ2๐ฅ+2 cosโก2๐ฅ ใ (ใโ๐๐๐ใโก(๐ /๐) ) ] = 1/2 [3+cosโกใ2๐ฅ+2 cosโก2๐ฅ ใ (โ1/2) ] = 1/2 [3+cosโกใ2๐ฅโ2 ร1/2รcosโก2๐ฅ ใ ] = ๐/๐ [๐+๐๐๐โกใ๐๐โ๐๐๐โก๐๐ ใ ] = 1/2 [3+0] = 3/2 = R.H.S. Hence, L.H.S. = R.H.S. Hence Proved