Question

Which of the following correctly expresses sin (70) + sin(30) as a product?

:
Select the correct answer below:
-2 sin (50)cos (20)
2sin (50)sin(20)
2sin(50)cos(20)
2sin(20)cos (50)​

Answer 1

2sin50 cos20

Explanation:

We need to write sin (70) + sin(30) as a product. The formula used here is :

`\sin A+\sin B=2\sin ((A+B)/(2))\cos((a-b)/(2))`

Here, A = 70 and B = 30

So,

`\sin 70+\sin 30=2\sin ((70+30)/(2))\cos((70-30)/(2))\\\\\sin 70+\sin 30=2\sin 50\cos20`

So, the value of sin (70) + sin(30) is 2sin50 cos20. Hence, the correct option is (c).