sin 25° cos 35° + cos 25° sin 35°
0.90630778703665
To solve this expression, we can use the trigonometric identity for the sine of the sum of two angles:
sin(A + B) = sin A * cos B + cos A * sin B
In this case, we have sin 25° cos 35° + cos 25° sin 35°.
By comparing this to the trigonometric identity, we can see that A = 25° and B = 35°. Therefore, we can rewrite the expression as:
sin(25° + 35°)
To find the value of sin(60°), we can use a reference angle. The reference angle for 60° is 30°.
We know that sin(30°) = 1/2.
Since we want the value of sin(60°), we can use the fact that sin(60°) = sin(180° - 60°).
This means that sin(60°) = sin(120°).
The sine function is positive in the second quadrant, so sin(120°) = sin(180° - 120°).
sin(180° - 120°) = sin(60°) = sin(30°) = 1/2.
Therefore, the value of sin 25° cos 35° + cos 25° sin 35° is 1/2.
To simplify the expression sin 25° cos 35° + cos 25° sin 35°, you can use the trigonometric identity for the sine of a sum of two angles:
sin(A + B) = sin A cos B + cos A sin B
Comparing this identity to our expression, we can see that:
A = 25° and B = 35°
So, sin 25° cos 35° + cos 25° sin 35° is equal to sin(25° + 35°).
Adding the angles together, we get:
sin(25° + 35°) = sin(60°)
Since sin(60°) is a well-known value, the final answer is:
sin 25° cos 35° + cos 25° sin 35° = sin(60°) = √3/2