If P_{n}=1+\cos 2^{n-1} \\theta-\sin 2^{n-1} \\theta and Q_{n}=1+\tan 2^{n-1} \\theta such that (P_{1} Q_{0}) \\times(P_{2} Q_{1}) \\times......(P_{n} Q_{n-1})=1for {n} \\to\infty, then value of {\\pi}/{\\theta.2^{n-1}} is

JEE Advanced 2021 Full Test 3 Paper 2

SECTION – C (Numerical Answer Type)
This section contains 06 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the SECOND DECIMAL PLACE; e.g. XXXXX. XX).

Question : 49 of 54

Marks: +1, -0

If Pn=1+cos‌2n−1‌θ−sin‌2n−1‌θ and Qn=1+tan‌2n−1‌θ such that (P1Q0)×(P2Q1)×......(PnQn−1)=1for n→∞, then value of

θ.2n−1

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