Question

If A+ B = π/4
Prove that
( cot A -1) (Cot B -1) = 2.​

Answer 1

Solution

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We have ,

A+B = π/4

taking cot both sides .

cot(A+B ) = cotπ/4

We know that

cot (a+b) = cot a cot b -1 / cot a +cot b.

Cot A cot B -1/ cot A + cot B = 1

cot A + cot B = cot A cot B -1

cot A cot B - cotA - cot B = 1

Adding 1 both sides.

cotA cotB - cot A - cot B +1 = 2

cot A ( cot B -1 ) -1 ( cotB - 1) = 2

(cot B -1 ) ( cot A -1 ) = 2 .

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Answer 2

$given \: a + b = \frac{\pi}{4}$