Question

sin(45°+A)=1/√2(sinA+cosA)​

Answer 1

Answer:

here L.H.S. = sin (45+A)

L.H.S.= sin 45×cos A + cos 45×sin A

$l.h.s. = \frac{1}{ \sqrt{2} } \cos \: a + \frac{1}{ \sqrt{2} } \sin \: a$

$l.h.s = \frac{1}{ \sqrt{2} } ( \cos \: a + \sin \: a)$

$l.h.s = r.h.s$

therefore,

$\sin( {45}^{0} + a) = \frac{1}{ \sqrt{2} } ( \sin \: a + \cos \: a)$