how would you find the exact value of this expression??
2sin15°cos°
To find the exact value of the expression 2sin15°cos°, we need to use the trigonometric identity for the product of two trigonometric functions.
The identity we will use is:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Based on this identity, we can rewrite the expression 2sin15°cos° by using the identity sin(A + B) with A = 0° and B = 15°:
2sin15°cos° = 2(sin(0° + 15°))
Now, we substitute the values into the identity:
2(sin(0° + 15°)) = 2(sin0°cos15° + cos0°sin15°)
Now, we can simplify further using the trigonometric values of sin0° and cos0°:
2(sin0°cos15° + cos0°sin15°) = 2(0cos15° + 1sin15°)
Since cos0° = 1 and sin0° = 0, the expression simplifies to:
2(0cos15° + 1sin15°) = 2(sin15°) = 2sin15°
Therefore, the exact value of the expression 2sin15°cos° is equal to 2sin15°.