Question

evaluate tan a = cot B prove that a + b = 90 degree​

Answer 1

in a right angled triangle ,right angled at c

tanA= BC/AC

cotB=BC/AC

data: tanA=cotB

tan(90-A)=cotB

cotA=cotB

AB/Bc=BC/AC

AC^ = BC^

AC=BC
∆ABC is an isosles right angled triangle. amgle opposite to equal sides are equal .
^A=^B= 180°/2=90°/2=45°
so,^A+^B=90°
hence proved

Answer 2

$\mathcal\red{Heyya}$❤

$\bf\red{\underline{Solution:-}}$

It is given that

tan A = cot B

⇒tan A=tan (90° −B )        

{ °•° cot B = tan ( 90° − B ) }

⇒A = 90° −B

⇒A + B= 90°

Hence Proved

$\bf\red{Thank\:You}$☺