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CBSE Class 11-science Answered

Prove that cos^2 pi/8 + cos^2 3pi/8 + cos^2 5pi/8 + cos^2 7pi/8 =2

 

Asked by anushkapanwar74 | 15 Aug, 2019, 01:26: PM
Expert Answer
cos2 ∏/8 + cos2 3∏/8 + cos2 5∏/8 + cos2 7∏/8 
Let ∏/8 = x then ∏ = 8x 
4x = ∏/2 ...(i)
LHS = cos2 ∏/8 + cos2 3∏/8 + cos2 5∏/8 + cos2 7∏/8 
= cos2 x + cos2 3x + cos2 5x + cos2 7x
= cos2 x + cos2 3x + cos2 (4x + x) + cos2 (4x + 3x)
= cos2 x + cos2 3x + cos2 (∏/2 + x) + cos2 (∏/2 + 3x)     from (i)
= cos2 x + cos2 3x + sin2 x + sin2 3x                              cos (∏/2 + x) = sin x
= cos2 x + sin2 x + cos2 3x + sin2 3x
= 1 + 1                                                                         cos2 x + sin2 x = 1
= 2
= RHS
Answered by Sneha shidid | 16 Aug, 2019, 09:45: AM
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