If $0 < \phi < \frac{\pi }{2},\;x = \mathop \sum \limits_{n = 0}^\infty {\cos ^{2n}}\phi ,\;y = \mathop \sum \limits_{n = 0}^\infty {\sin ^{2n}}\phi $ and $z = \mathop \sum \limits_{n = 0}^\infty {\cos ^{2n}}\phi {\sin ^{2n}}\phi $, then

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Hard

1 of 1

Analyzing +4 | -1

0 < \phi < \frac{\pi }{2},\;x = \sum \limits_{n = 0}^\infty {\cos ^{2n}}\phi ,\;y = \sum \limits_{n = 0}^\infty {\sin ^{2n}}\phi

and

z = \sum \limits_{n = 0}^\infty {\cos ^{2n}}\phi {\sin ^{2n}}\phi

, then

View answer and explanation

Correct option: B

xyz = xy + z

Option B (

xyz = xy + z

) is correct because it is derived by expressing

x

y

, and

z

in terms of

\sin^2{\phi}

and

\cos^2{\phi}

and then simplifying the equation.

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A P

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\frac{3}{4}