Simplify cos of two 𝑋 times cos of
22𝑋 minus sin of two 𝑋 times sin of 22𝑋.
When we look at this expression, we
see that we have the angle two 𝑋 and the angle 22𝑋. We have the cos and sin of the
angle two 𝑋, and we have the cos and sin of the angle 22𝑋, which means we have an
expression in the form cos of 𝐴 times cos of 𝐵 minus sin of 𝐴 times sin of
𝐵. And we can simplify this expression
using the angle sum identities. We know that the cos of 𝐴 times
the cos of 𝐵 minus the sin of 𝐴 times the sin of 𝐵 is equal to the cos of 𝐴 plus
𝐵. In our case, the angle 𝐴 is two 𝑋
and the angle 𝐵 is 22𝑋, making this expression equal to cos of two 𝑋 plus 22𝑋,
cos of 24𝑋. And so the simplified form of this
expression is cos of 24𝑋.