Question

F) If cosa + sinß = a and sina + cosß = b. prove that: sin(a + B) = (a²+ b² - 2).​

Answer 1

Hi,

Explanation:

`Remember:\\(x+y)^2=x^2+y^2+2xy\\sin(x+y)=sin(x)cos(y)+cos(x)sin(y)\\\\\left\{\begin{array}{ccc}cos(a)+sin(b)&=&A\\sin(a)+cos(b)&=&B\\\end{array}\right.\\\\\\\\\boxed{A^2+B^2-2}\\=(cos(a)+sin(b))^2 + (sin(a)+cos(b))^2-2\\\\=cos^2(a)+sin^2(b)+2cos(a)sin(b)+sin^2(a)+cos^2(b)+2sin(a)cos(b)-2\\\\=1+1-2+2(sin(a)cos(b)+cos(a)sin(b) )\\\\=\boxed{2\ sin(a+b)}\\\\`