Cos(21)cos(9)-sin(21)sin(9)
have you come across this formula ?
cos(A+B) = cosAcosB - sinAsinB
your expression matches this
Cos(21)cos(9)-sin(21)sin(9)
= cos(21+9)
= cos30
= √3/2
To calculate the value of the expression cos(21)cos(9) - sin(21)sin(9), you can use the trigonometric identity called the angle addition formula. According to this formula, the cosine of the difference of two angles (θ - φ) can be expressed as the product of the cosines of the individual angles plus the product of the sines of the individual angles.
The angle addition formula is:
cos(θ - φ) = cos(θ)cos(φ) + sin(θ)sin(φ)
In this case, θ is 21 and φ is 9. So, you can rewrite the original expression as:
cos(21)cos(9) - sin(21)sin(9) = cos(21 - 9)
Now, calculate the difference of the angles:
21 - 9 = 12
So, the expression becomes:
cos(12)
To find the value of cos(12), you can use a calculator or trigonometric tables.