Question

If A+B = π/4 then value of (CotA -1) (CotB - 1) =?​

Answer 1

Question:-

$\bf \:If A + B = \dfrac{\pi}{4}, \: find \: (cotA - 1)(cotB - 1)$

$\bf\underbrace\orange{Answer:}$

Given :-

$\bf \:A + B = \dfrac{\pi}{4}$

To find :-

• The value of (cotA - 1)(cotA + 1)

Formula used :-

$\bf \:cot(A - B) = \dfrac{cotAcotB + 1}{cotB - cotA}$

$\bf\underbrace\orange{Solution:}$

$\bf \:A + B = \dfrac{\pi}{4}$

$\bf\implies \:B = \dfrac{\pi}{4} - A$

Consider

$\bf \:(cotA - 1)(cotB - 1)$

Put the value of B, we get

$\bf\implies \:(cotA - 1)(cot(\dfrac{\pi}{4} - A)- 1)$

$\bf\implies \:(cotA - 1)(\dfrac{cot\dfrac{\pi}{4} cotA + 1}{cotA - cot\dfrac{\pi}{4} } - 1)$

$\bf\implies \:(cotA - 1)(\dfrac{cotA + 1}{cotA - 1} - 1)$

$\bf\implies \:(cotA - 1)(\dfrac{cotA + 1 - cotA + 1)}{cotA - 1}$

$\bf\implies \:2$

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