Question

Sin 15+ sin 75=

1.√3/2 2. √3/√2 3. 2/√3 4.1/√3

Answer 1

correct answer is
$\frac{ \sqrt{3} }{ \sqrt{2} ?}$
see this method. thank you

Answer 2

sin 15 = sin(60-45)

= sin 60 cos 45 - cos 60 sin 45  ( sin (A-B) = Sin A cos B - cos A sin B)

= root 3/2 * root 2/2 - 1/2 * root 2/2(sin 45 = 1/root 2 can be written as root 2/2)

= root 6/4 - 1/2 * root 2/2

= root 6 - root 2/4   ----------------- (1)




Sin 75 = sin(30 + sin 45)

= sin 30 cos 45 + cos 30 sin 45  (Sin (A+B) = Sin A cos B + Cos A Sin B)

= 1/2 * root 2/2 + root 3/2 * root 2/2

= root 2 + root 6/4   ----------------- (2)


sin 15 + sin 75

= root 6 - root 2/4 + root 2 + root 6/4

= 2 root 6/4

= root 6/2

= root 3/root 2.



Hope this helps!