jee-main 2021 Q64

jee-main · India · session1_25feb_shift1 Geometric Sequences and Series Geometric Series with Trigonometric or Functional Terms

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

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

Paper Questions

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