Question

cosA+sinA=√2sin(90-A) change to cotA

Answer 1

Cos A + Sin A = √2 × Sin ( 90 - A )

Cos A + Sin A = √2 × Cos A

Sin A = √2 × Cos A - Cos A

Sin A = Cos A ( √2 - 1 )

$1 = \frac{ Cos A ( \sqrt{2} - 1 )}{Sin \: A} \\ \\ Cot \: A \: = \frac{1}{( \sqrt{2} - 1) }$

$\\ Cot \: A = \frac{1×(\sqrt{2} + 1 )}{(\sqrt{2} - 1 ) (\sqrt{2} + 1 )} \\ \\ Cot \: A = \frac{(\sqrt{2} + 1 )}{2 - 1 } \\ \\ Cot \: A = (\sqrt{2} + 1 )$