cos 75 degrees * cos 15 degrees - sin 75 degrees sin 15 degrees is equivalent to
To find the value of cos 75 degrees * cos 15 degrees - sin 75 degrees * sin 15 degrees, we can use the trigonometric identity known as the cosine of the difference of angles.
The cosine of the difference of two angles (A - B) can be expressed as follows:
cos (A - B) = cos A * cos B + sin A * sin B
In this case, A = 75 degrees and B = 15 degrees. Substituting these values into the identity, we have:
cos (75 degrees - 15 degrees) = cos 75 degrees * cos 15 degrees + sin 75 degrees * sin 15 degrees
Now, let's substitute the given values back into the equation:
cos (75 degrees - 15 degrees) = cos 75 degrees * cos 15 degrees - sin 75 degrees * sin 15 degrees
So, cos 75 degrees * cos 15 degrees - sin 75 degrees * sin 15 degrees is equivalent to cos (75 degrees - 15 degrees).
To simplify this expression, we can use the trigonometric identity for the product of two cosines and the difference of two sines:
cos(α) * cos(β) - sin(α) * sin(β) = cos(α - β)
Therefore, cos(75 degrees) * cos(15 degrees) - sin(75 degrees) * sin(15 degrees) is equivalent to cos(75 degrees - 15 degrees).
Simplifying further:
75 degrees - 15 degrees = 60 degrees
So, cos(75 degrees) * cos(15 degrees) - sin(75 degrees) * sin(15 degrees) is equivalent to cos(60 degrees).
recall that cos(A+B) = cosA cosB - sinA sinB
So, what do you think?