Question

plz explain it properly. I will mark it as brainalist​

Answer 1

hope it helps plzz mark brainliest

Answer 2

Given :-

• Sin (A-B)= 1/2

• Cos(A+B)=1/2

To find :-

we have to find the value of A and B

Now

A.T.Q :-

$\sf\:\: Sin(A-B)=\dfrac{1}{2}\\ \\ \sf\:\:and\:\:Sin30{}^{\circ}=\dfrac{1}{2}\\ \\ \sf\:\:So,\:\:we\: can\: write\:Sin30{}^{\circ}\:\:in\:place\:of\:\dfrac{1}{2}\\ \\ \sf\implies Sin(A-B)=Sin30{}^{\circ}\\ \\ \sf\implies A-B=30{}^{\circ}-------(i)$

$\sf\:\: Cos(A+B)=\dfrac{1}{2}\\ \\ \sf\:\:\: \bullet Cos60{}^{\circ}=\dfrac{1}{2}\\ \\ \sf\implies Cos(A+B)=Cos60{}^{\circ}\\ \\ \sf\implies A+B=60{}^{\circ}-------(ii)\\ \\ \sf\:\:\:\: {\dag{Add\: equation\:(i)\:\:and\:\:(ii)}}$

$\sf\implies A\cancel{-B}+A\cancel{+B}=30{}^{\circ}+60{}^{\circ}\\ \\ \sf\implies 2A=90{}^{\circ}\\ \\ \sf\implies A=\cancel{\dfrac{90}{2}}\\ \\ \sf\implies A=45{}^{\circ}$

• A=45°
• B=?
• Put the value of A in equation (i)

$\sf\implies A-B=30{}^{\circ}\\ \\ \sf\implies 45{}^{\circ}-B=30{}^{\circ}\\ \\ \sf\implies 45{}^{\circ}-30{}^{\circ}=B\\ \\ \sf\implies 15{}^{\circ}=B$

$\boxed{\sf{\therefore A=45{}^{\circ}}}$

$\boxed{\sf{\therefore B=15{}^{\circ}}}$