Question

WHY IS SIN (A+B) NOT EQUAL TO SIN A + SIN B

Answer 1

sin[a+b]≠sina+sinb
let us imagine a=30,b=60
findLHS
sin[a+b]
=sin[30+60]
=sin [90]
=1/2
find RHS
sina+sinb
=sin30+sin60
=1/2+√3/2
=(1+√3)/2
⇒1/2≠(1+√3)/2
∴sin[a+b]≠sina+sinb

Answer 2

$\Huge\bf\maltese{\underline{\green{Answer}}}\maltese$

$\implies$$\large\bf{\underline{\red{VERIFIED✔}}}$

$sin(a + b) = sin \: a + sin \: b \\ \\let \: a = {30}^{0} \: and \: b = {60}^{0} \\ \\ \sin( {30}^{0} + {60}^{0}) = \sin{30}^{0} + \sin {60}^{0} \\ \\ \sin {90}^{0} = \sin {30}^{0} + \sin {60}^{0} \\ \\ 1 = \frac{1 + \sqrt{3} }{2} \\ \\ 1≠ \frac{1 + \sqrt{3} }{2} \\ \\ = > false. \\ \\ so. \: sin(a + b) ≠sin \: a + sin \: b$

• I Hope it's Helpful My Friend.