Question

write down the expansion of sin(A+B) and hence find sin 15 deg in simplest surd form

Answer 1

sin(A+B) = sinAcosB + cosAsinB

Answer 2

sin(15) = sin(45-30)
use sin(A-B) = sin A cos B - sin B cos A

put
A = 45 and B = 30

Answer 3

Got that ?

Answer 4

no im learning this for the first time

Answer 5

does it equal 0

Answer 6

But here @vishweshshrimali5 you will use sin(A-B) formula..

Answer 7

\[\sin(A-B) = \sin(A) \cdot \cos(B) - \cos(A) \cdot \sin(B)\]

For 15 degree you will select A = 45 and B = 30..

Answer 8

\[\sin(45 - 30) = \sin(45) \cdot \cos(30) - \cos(45) \cdot \sin(30)\]

Answer 9

is it right to put sin 15deg =0 in simplest form

Answer 10

or is it better left as is

Answer 11

Now use this values and try to find out the value:

\[\sin(45) = \frac{\sqrt{2}}{2}\]
\[\cos(45) = \frac{\sqrt{2}}{2}\]
\[\sin(30) = \frac{1}{2}\]
\[\cos(30) = \frac{\sqrt{3}}{2}\]

Put this values on Right Hand side and solve it..

Leave Left Hand Side as such..

Answer 12

what value am i looking for is it pi/4, -pi/4, pi/6, -pi/6

Answer 13

No..

Just do what I said..

Put those values in the formula that I gave you :

\[\sin(45) \cdot \cos(30) - \cos(45) \cdot \sin(30)\]

Here put those values..