What-the-value-of-1-cot-23-1-cot-22-

Question Number 135795 by benjo_mathlover last updated on 16/Mar/21

W h a t t h e v a l u e o f (1 - \cot 23 °) (1 - \cot 22 °) .

Answered by MJS_new last updated on 16/Mar/21

(1 - \cot (\frac{45}{2} - x)) (1 - \cot (\frac{45}{2} + x)) = 2

Answered by liberty last updated on 16/Mar/21

\cot 22 ° = \cot (45 ° - 23 °)

\cot 22 ° = \frac{1}{\tan (45 ° - 23 °)} = \frac{1}{\frac{1 - \tan 23 °}{1 + \tan 23 °}}

\cot 22 ° = \frac{1 + \tan 23 °}{1 - \tan 23 °}

s o 1 - \cot 22 ° = 1 - \frac{1 + \tan 23 °}{1 - \tan 23 °} = - \frac{2 \tan 23 °}{1 - \tan 23 °}

t h e n (1 - \frac{1}{\tan 23 °}) (- \frac{2 \tan 23 °}{1 - \tan 23 °})

= \frac{\tan 23 ° - 1}{\tan 23 °} \times \frac{- 2 \tan 23 °}{1 - \tan 23 °} = 2

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