Question

Use a sum or difference identity to find the exact value. sin 10° cos 50° + cos 10° sin 50°​

Answer 1

Answer:

= √3/2

Explanation:

We can use the sum identity for the sine of the sum of two angles to simplify the expression:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

In this case, let a = 10° and b = 50°. Then we have:

sin(10° + 50°) = sin(10°) cos(50°) + cos(10°) sin(50°)

The value of sin(10° + 50°) can be calculated using the sum-to-product identity for the sine function:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

sin(10° + 50°) = sin(10°) cos(50°) + cos(10°) sin(50°)

sin(60°) = sin(10°) cos(50°) + cos(10°) sin(50°)

sqrt(3)/2 = sin(10°) cos(50°) + cos(10°) sin(50°)

Therefore, the exact value of the expression is:

sin 10° cos 50° + cos 10° sin 50° = sqrt(3)/2

We can write it as:

sin 10° cos 50° + cos 10° sin 50° = √3/2

So, the answer is √3/2.

Answer 2

√3/2

Explanation:

sin(10°) • cos(50°) + cos(10°) • sin(50°)

= sin(10 + 50)

sin(60°) = √3/2