Question

Sina+sinb=√3/√2
Cosa+cosb=1/√2
Find A

Answer 1

$( \sin(a) + \sin(b) ) {}^{2} = { \sin }^{2} a + { \sin }^{2} b + 2 \sin(a) \sin(b) \\ {( \cos(a) + \cos(b)) }^{2} = { \cos}^{2} a + { \cos }^{2} b + 2 \cos(a) \cos(b) \\ add \\ ( \sqrt{3 \div 2} { }^{2} + \sqrt{1 \div 2 {}^{2} } ) = (1) + (1) + 2( \sin(a) \sin(b) + \cos(a) \cos(b) ) \\ 2 = 2 + 2( \cos(a - b) ) \\ \cos(a - b) = 0 \\ a - b = 90 \\ \\ a = 90 + b \\ it \: is \: given \: cosa + cosb = 1 \div \sqrt{2} \\ cos(90 - b) + cosb = 1 \div \sqrt{2} \\ 2cosb = 1 \div \sqrt{2 } \\ cosb = 1 \div (2 \sqrt{2)} \\ cosa = 1 \div \sqrt{2} - cosb \\ cosa = (1 \div 2 \sqrt{2} ) \\ a = cos ^{ - 1} (1 \div 2 \sqrt{2)}$
here is complete solution... I think there was problem in question in sina+sinb=.√3/2