y=1+cos2θ+cos4θ+…
Above series is an infinite G.P, apply sum of infinite G.P.
⇒y=1−cos2θ1
⇒y1=sin2θ
x=1−(−tan2θ)1=sec2θ1
⇒cos2θ=x
⇒y1+x=1
⇒y(1−x)=1
If x=n=0∑∞(−1)ntan2θ and y=n=0∑∞cos2nθ, for 0<θ<4π, then:
Held on 9 Jan 2020 · Verified 6 Jul 2026.
x(1+y)=1
y(1−x)=1
y(1+x)=1
x(1−y)=1
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