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JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
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
- A \(x y-z=(x+y) z\)
- B \(x y+y z+z x=z\)
- C \(xyz =4\)
- D \(x y+z=(x+y) z\)
Answer & Solution
Correct Answer
(D) \(x y+z=(x+y) z\)
Step-by-step Solution
Detailed explanation
\(x =\frac{1}{1-\cos ^{2} \theta} \Rightarrow \sin ^{2} \theta=\frac{1}{ x }\) Also, \(\cos ^{2} \theta=\frac{1}{y} \& 1-\sin ^{2} \theta \cos ^{2} \theta=\frac{1}{z}\) So, \(1-\frac{1}{x} \times \frac{1}{y}=\frac{1}{z} \Rightarrow z(x y-1)=x y \quad \ldots(1)\) Also,…
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