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$If a_{n + 1} = \sqrt{\frac{1}{2} (1 + a_{n})}, then \cos (\frac{\sqrt{1 - a_{0}^{2}}}{a_{1} a_{2} \dots \dots \infty}) =$

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detailed solution

Correct option is C

We havean+1=1+an2 Let a0=cosθ⇒a1=1+cosθ2=cosθ2⇒a2=cosθ4⇒a3=cosθ8⇒an+1=cosθ2n+1 and so onWe know that cosθ2cosθ22cosθ23..............cosθ2n−1+............∞=sinθθ∴cos1-a02a1a2……∞=cossinθsinθ·θ =cosθ=a0

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If an+1=121+an, then cos1-a02a1a2……∞=

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$If a_{n + 1} = \sqrt{\frac{1}{2} (1 + a_{n})}, then \cos (\frac{\sqrt{1 - a_{0}^{2}}}{a_{1} a_{2} \dots \dots \infty}) =$