If cosx2⋅cosx22⋅cosx23⋯∞=sinxx,x∈(0,π2), then 122sec2x2+124 – InterviewSolution

1.	If cosx2⋅cosx22⋅cosx23⋯∞=sinxx,x∈(0,π2), then 122sec2x2+124sec2x22+126sec2x23⋯∞ is equal to
Answer» If $cos \frac{x}{2} \cdot cos \frac{x}{2^{2}} \cdot cos \frac{x}{2^{3}} \dots \infty = \frac{sin x}{x}, x \in (0, \frac{π}{2})$ , then $\frac{1}{2^{2}} {sec}^{2} \frac{x}{2} + \frac{1}{2^{4}} {sec}^{2} \frac{x}{2^{2}} + \frac{1}{2^{6}} {sec}^{2} \frac{x}{2^{3}} \dots \infty$ is equal to

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