Evaluate sin(29 degrees)cos(31 degrees) + cos(29 degrees)sin(31 degrees) exactly, without using a calculator.
sqrt(3)/2
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To evaluate the expression sin(29°)cos(31°) + cos(29°)sin(31°) exactly without using a calculator, we can use the trigonometric identity known as the angle addition formula:
sin(A + B) = sin A * cos B + cos A * sin B
By comparing this identity with the given expression, we can see that sin(29°)cos(31°) + cos(29°)sin(31°) is equivalent to sin(29° + 31°).
Now, we can simplify sin(29° + 31°) by adding the angles inside the sine function:
sin(29° + 31°) = sin(60°)
Since the sine of 60° is a well-known value, we can evaluate the expression exactly:
sin(60°) = √3 / 2
Therefore, sin(29°)cos(31°) + cos(29°)sin(31°) = √3 / 2.
Correct!
sin(a)cos(b)+cos(a)sin(b)
=sin(a+b)
Let a=29°, b=31°
so the expression represents sin(60°)=(√3)/2