Question

(37.5)°x cos (7.5)°​

Answer 1

Step-by-step explanation:

You can use the formula for cosine of sum and difference of two angles:

cos(a+b)=cos(a)cos(b) - sin(a)sin(b)

cos(a-b)=cos(a)cos(b) + sin(a)sin(b)

Therefore

cos(a+b)+cos(a-b) = 2 cos(a)cos(b)

Rearranging to

cos(a)cos(b)=1/2*(cos(a+b)+cos(a-b))

Substituting a = 37.5 and b = 7.5 (I assume you are working in degrees)

cos(37.5)cos(7.5) = 1/2*(cos(37.5+7.5)+cos(37.5-7.5))

Here

cos(37.5+7.5)=cos(45)=√2/2

cos(37.5-7.5)=cos(30)=√3/2

And finally

cos(37.5)cos(7.5)=1/2(√2/2+√3/2)=1/4(√3+√2)