jee-main 2020 Q55

jee-main · India · session1_09jan_shift2 Geometric Sequences and Series Geometric Series with Trigonometric or Functional Terms

If $x = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \tan ^ { 2 } \theta$ and $y = \sum _ { n = 0 } ^ { \infty } \cos ^ { 2 n } \theta$, for $0 < \theta < \frac { \pi } { 4 }$, then:
(1) $x ( 1 + y ) = 1$
(2) $y ( 1 - x ) = 1$
(3) $y ( 1 + x ) = 1$
(4) $x ( 1 - y ) = 1$

If $x = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \tan ^ { 2 } \theta$ and $y = \sum _ { n = 0 } ^ { \infty } \cos ^ { 2 n } \theta$, for $0 < \theta < \frac { \pi } { 4 }$, then:\\
(1) $x ( 1 + y ) = 1$\\
(2) $y ( 1 - x ) = 1$\\
(3) $y ( 1 + x ) = 1$\\
(4) $x ( 1 - y ) = 1$

Paper Questions

Q51 Q52 Q53 Q54 Q55 Q56 Q57 Q58 Q59 Q60 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68