Question

If sin (x+y) =1÷2 and cos (x-y)= 1÷2 then what is the value of x and y?

Answer 1

Answer:

$\huge\underline{ \underline{ \red { \bigstar \: your \: \: \: answer \: \: \bigstar}}}$

Step-by-step explanation:

$\bf\pink{ \mapsto:sin(x + y) = \frac{1}{2} } \\ \\ \bf\orange{ \implies: sin(x + y) = sin30 \degree} \\ \\ \bf\pink{ \implies:x + y= 30 \degree \: \: - - - - - - (1) } \\ \\ \bf\purple{ cos(x - y) = cos \: \frac{1}{2} } \\ \\ \bf\red{ \implies:cos \: (x - y)= cos \: 60 \degree } \\ \\ \bf\blue{ \implies:x - y = 60 \degree - - - - - - (2) } \\ \\ \bf\orange{ \underline{ using \: elimination \: method} } \\ \\ \bf\pink{(2) - (1) \implies} \\ \\ \bf\green{ \implies:(x - y) - (x + y) = 60\degree - 30\degree } \\ \\ \bf\red{ \implies: x - y - x - y = 30 \degree} \\ \\ \bf\red{ \implies: - 2y = 30 \degree } \\ \\ \bf\purple{ \implies: y = - \frac{30 \degree}{2} } \\ \\ \bf\pink{ \underline{ \boxed{ \implies: y = - 15 \degree}}} \\ \\ \bf\red{ \underline{value \: of \: y \: put \: in \: (1)}} \\ \\ \bf\red{ (1)\implies \: x + y = 30 \degree} \\ \\ \bf\red{ \implies: x + ( - 15 \degree) = 30 \degree} \\ \\ \bf\red{ \implies:x = 30 \degree + 15 \degree } \\ \\ \bf\red{ \underline{ \boxed{ \implies: x = 45 \degree}}}$

$\large\boxed{ \fcolorbox{yellow}{lime}{hope \: it \: help \: you}}$