Question

If $\tan (A-B)=\frac{1}{\sqrt{3}}$ and $\sin A=\frac{1}{\sqrt{2}}$ then the value of B is

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (A)

${15}^{\circ }$

$\Rightarrow$ We have, $sinA=\frac{1}{\sqrt{2}}$

$\therefore$ $A=si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$

$\therefore$ $A={45}^o$ -------- ( 1 )

$\Rightarrow$ Now, $tan(A-B)=\frac{1}{\sqrt{3}}$

$\Rightarrow$ $A-B=ta{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\therefore$ $A-B={30}^o$

$\therefore$ ${45}^o-B={30}^o$ [ From( 1 ) ]

$\therefore$ $B={45}^o-{30}^o$

$\therefore$ $B={15}^o$