Question

Let A = 30 & B = 60. Verify each of the following sin(A-B)=sinA.cosB-cosA.sinB​

Answer 1

Step-by-step explanation:

sin(30-60)

=sin (-30) [sin (-theta) = - sin ( theta)]

= -sin(30)

= - 1/2

sin(30). cos(60)- cos(30). sin(60)

1/2×1/2-√3/2.√3/2

1/4-3/4

-2/4

-1/2

hence proved

hope this helps

Answer 2

Step-by-step explanation:

A=30

B=60

$\sin(a - b) = \sin(a) \cos(b) - \cos(a) \sin(b)$

lhs=

$\sin(a - b) = \sin(30 - 60)$

$= \sin( - 30)$

$= - \sin(30)$

$= - \frac{1}{2}$

$rhs = \sin(a) \cos(b) - \cos(a) \sin(b)$

$= \sin(30) \cos(60) - \cos(30) \sin(60)$

$= \frac{1}{2} . \frac{1}{2} - \frac{ \sqrt{3} }{2} . \frac{ \sqrt{3} }{2}$

$= \frac{1}{4} - \frac{3}{4}$

$= - \frac{1}{2}$

therefore LHS=RHS