Question

For 0 <θ<π/2, if x =

$\sum_{n = 0}^{\infty}{\cos^{2n}\theta,}y = \sum_{n = 0}^{\infty}{\sin^{2n}\theta,}z = \sum_{n = 0}^{\infty}{\cos^{2n}\theta\sin^{2n}\theta,}$ then

• A. xyz = xz + y
• B. xyz = xy +z
• C. xyz = yz +x
• D. None of these

Answer 1

Answer: (B)

xyz = xy +z

Answer 2

Here x = $\frac{1}{1 - \cos^{2}\theta}$ = cosec²θ , y = sec² θ ,

z = $\frac{1}{1 - \sin^{2}\theta\cos^{2}\theta}$

z =$\frac{1}{1 - \frac{1}{x}.\frac{1}{y}} = \frac{xy}{xy - 1}$ ⇒ xyz = xy + z