cos15°cos30°- sin15°sin30° =
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To calculate the expression cos(15°)cos(30°) - sin(15°)sin(30°), we can use the trigonometric identity known as the angle sum formula for cosine and sine.
The angle sum formula for cosine states that:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Similarly, the angle sum formula for sine states that:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
In our expression, we have cos(15°)cos(30°) - sin(15°)sin(30°). We can rewrite 30° as the sum of 15° and 15°, so that we can apply the angle sum formulas.
cos(15°)cos(30°) - sin(15°)sin(30°) = cos(15°)(cos(15°)cos(15°) - sin(15°)sin(15°))
Now, let's use the angle sum formulas:
cos(15°)(cos(15°)cos(15°) - sin(15°)sin(15°))
= cos(15°)cos^2(15°) - cos(15°)sin^2(15°)