Question

If tanA=cotB, Prove that A+B=90°

Answer 1

$\huge\underline\mathbb{\red S\pink {O}\purple {L} \blue {UT} \orange {I}\green {ON :}}$

TanA = cot(90-A)

Put value in given expression

cot(90-A) = cotB

Therfore

90-A=B

A+B = 90

$\huge\underline\mathbb{\red F\pink {O}\purple {L} \blue {LO} \orange {W}\green {ME :}}$

Answer 2

$\huge\tt{Answer:-}$

$\sf tanA = cotB$

$\color{lime} \boxed{\sf As, \: we \: know \: that \: tanA = cot(90°-A)}$

$\sf ➝ \: cot(90°-A) = cotB$

$\sf ➝ \: \cancel{cot}(90°-A) = \cancel{cot}B$

$\sf ➝ \: 90°-A=B$

$\sf ➝ \: A+B = 90°$

$\color{cyan} \boxed{\sf A+B = 90°}$