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Question Number 119839 by ZiYangLee last updated on 27/Oct/20

Prove that sin x−cos^2 x+sin^3 x−cos^4 x+sin^5 x−cos^6 x +sin^7 x−cos^8 x+……=(√2)−1

Provethatsinx−cos2x+sin3x−cos4x+sin5x−cos6x+sin7x−cos8x+……=2−1

Answered by TANMAY PANACEA last updated on 27/Oct/20

sinx=a cosx=b a^2 +b^2 =1 S=(a+a^3 +a^5 +a^7 +...)−(b^2 +b^4 +b^6 +b^8 +...) =((a(1−a^(2n) ))/(1−a^2 ))−((b^2 (1−b^(2n) ))/(1−b^2 )) when n→∞ S_n =(a/(1−a^2 ))−(b^2 /(1−b^2 )) wait

sinx=acosx=ba2+b2=1S=(a+a3+a5+a7+...)−(b2+b4+b6+b8+...)=a(1−a2n)1−a2−b2(1−b2n)1−b2whenn→∞Sn=a1−a2−b21−b2wait

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