JEE PYQ: Trigonometric Ratios And Identities Question 7
Question 7 - 2020 (09 Jan Shift 2)
If $x = \sum_{n=0}^{\infty} (-1)^n \tan^{2n} \theta$ and $y = \sum_{n=0}^{\infty} \cos^{2n} \theta$, for $0 < \theta < \frac{\pi}{4}$, then:
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(1) $x(1 + y) = 1$
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(2) $y(1 - x) = 1$
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(3) $y(1 + x) = 1$
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(4) $x(1 - y) = 1$
Show Answer
Answer: (2) $y(1 - x) = 1$
Solution
$y = \frac{1}{\sin^2\theta}$, $x = \cos^2\theta$. So $y(1-x) = \frac{1}{\sin^2\theta} \cdot \sin^2\theta = 1$.
BETA
