Question

maths legend

please help​

Answer 1

Answer:

$A+B= \frac{\pi }{4}$

Step-by-step explanation:

$Sin \: A = \frac{1}{\sqrt{10}}$

$\implies Cos\:A = \sqrt{1 - Sin^{2}A }$

$\implies \: \: \: \: \: \:  = \sqrt{1 - \frac{1}{10} }$

$\implies \: \: \: \: \: \: = \sqrt{\frac{10 - 1}{10} }$

$\implies \: \: \: \: \: \: = \sqrt{\frac{9}{10} }$

$\implies \: \: \: \: \: \: = \frac{3}{\sqrt{10} }$

$Sin \: B = \frac{1}{\sqrt{5}}$

$\implies Cos\:B = \sqrt{1 - Sin^{2}B }$

$\implies \: \: \: \: \: \:= \sqrt{1 - \frac{1}{5} }$

$\implies \: \: \: \: \: \: = \sqrt{\frac{5 - 1}{5} }$

$\implies \: \: \: \: \: \: = \sqrt{\frac{4}{5} }$

$\implies \: \: \: \: \: \: = \frac{2}{\sqrt{5} }$

$Since,\: Sin(A+B) = Sin\:A\:Cos B + Cos\:A\:Sin\:B$

$\:\:\:\:\:\:\:\:\:\:\:\: = \frac{1}{\sqrt{10}}*\frac{2}{\sqrt{5}} + \frac{3}{\sqrt{10}}*\frac{1}{\sqrt{5}}$

$= \frac{2}{\sqrt{50} } + \frac{3}{\sqrt{50} }$

$= \frac{5}{\sqrt{50} }$

$= \frac{5}{5\sqrt{2} }$

$= \frac{1}{\sqrt{2} }$

$Sin(A+B) = \frac{1}{\sqrt{2} }$

$\implies A+B= \frac{\pi }{4}$

Answer 2

Answer is in attachment

thank you