Question

If tanA = cotB , Prove thet A + B = 90°

Answer 1

$\textbf{Given:}$

$\tan{A}=\cot{B}$

$\textbf{To prove:}$

$A+B=90^{\circ}$

$\textbf{Solution:}$

$\text{Consider,}$

$\tan{A}=\cot{B}$

$\dfrac{\sin{A}}{\cos{A}}=\dfrac{\cos{B}}{\sin{B}}$

$\sin{A}\,\sin{B}=\cos{A}\,\cos{B}$

$\cos{A}\,\cos{B}-\sin{A}\,\sin{B}=0$

$\text{Using the identity}$

$\boxed{\bf\,cos(A+B)=cosA\,cosB-sinA\,sinB}$

$\cos{(A+B)}=0$

$\implies\bf\,A+B=90^{\circ}$

$\text{Hence proved}$

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Answer 2

Answer:

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