Mathematics: If sin (A+B)=1 and tan (A-B)=1/sqroot 3 are acute angles. find out the value of A and B

If sin (A+B)=1 and tan (A-B)=1/sqroot 3 are acute

Ответ:

mai1261

11.07.2021

A = 60° , B = 30°

Step-by-step explanation:

$sin(A+B ) = 1\\\\\ \ \ (A + B) \ = \ \ sin^{-1} 1\\\\A + B = 90^\circ --(1)\\\\ \ tan (A - B) = \frac{1}{\sqrt{3}}\\\\(A-B) = tan^{-1}\frac{1}{\sqrt3}}\\\\A - B = 30^\circ --(2)\\\\ (1) + (2) = 2A = 120^\circ\\$

$A = 60^\circ$

$from \ (1) \\A + B = 90^\circ\\60^\circ + B = 90^\circ\\B = 90^\circ - 60^\circ\\B = 30^\circ$

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Ответ:

aangellexith4237

25.04.2023

Mathematics

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If sin (A+B)=1 and tan (A-B)=1/sqroot 3

are acute angles. find out the value of A and B

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If sin (A+B)=1 and tan (A-B)=1/sqroot 3 are acute angles. find out the value of A and B​

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If sin (A+B)=1 and tan (A-B)=1/sqroot 3

are acute angles. find out the value of A and B