# 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, 13:26: PM

Expert Answer

cos

^{2}∏/8 + cos^{2}3∏/8 + cos^{2}5∏/8 + cos^{2}7∏/8Let ∏/8 = x then ∏ = 8x

4x = ∏/2 ...(i)

LHS = cos

^{2}∏/8 + cos^{2}3∏/8 + cos^{2}5∏/8 + cos^{2}7∏/8= cos

^{2}x + cos^{2}3x + cos^{2}5x + cos^{2}7x= cos

^{2}x + cos^{2}3x + cos^{2}(4x + x) + cos^{2}(4x + 3x)= cos

^{2}x + cos^{2}3x + cos^{2}(∏/2 + x) + cos^{2}(∏/2 + 3x) from (i)= cos

^{2}x + cos^{2}3x + sin^{2}x + sin^{2}3x cos (∏/2 + x) = sin x= cos

^{2}x + sin^{2}x + cos^{2}3x + sin^{2}3x= 1 + 1 cos

^{2}x + sin^{2}x = 1= 2

= RHS

Answered by Sneha shidid | 16 Aug, 2019, 09:45: AM

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