First slide

Compound angles

Question

$(1 - \cot 1^{o}) (1 - \cot 2^{o}) (1 - \cot 3^{o}) ............... (1 - \cot 44^{o}) = 2^{n}, t h e n n =$

Moderate

A

11
B

22
C

44
D

$\sqrt{22}$

Solution

$\begin{array}{l} If A + B = \frac{π}{4} then (1 - \cot A) (1 - \cot B) = 2 \\ N o w (1 - \cot 1 °) (1 - \cot 2 °) (1 - \cot 3 °) \dots \dots \dots . . (1 - \cot 43 °) (1 - \cot 44 °) = 2^{n} \\ \Rightarrow (1 - \cot 1 °) (1 - \cot 44 °) (1 - \cot 2 °) (1 - \cot 43 °) . . . . (1 - \cot 22 °) (1 - \cot 23 °) = 2^{n} \\ \Rightarrow 2^{22} = 2^{n} \\ \Rightarrow n = 22 \end{array}$

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