Question

Cos52cos78-sin52sin78​

Answer 1

Cos52⁰Cos78⁰ - Sin52⁰Sin78⁰ = Сos(52⁰ + 78⁰) = Cos130⁰ =

= Cos(90⁰ + 40⁰) = - Sin40⁰

Answer 2

To simplify the expression cos(52°)cos(78°) - sin(52°)sin(78°), we can use the trigonometric identity for the difference of cosines:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Let A = 52° and B = 78°:

cos(52°)cos(78°) - sin(52°)sin(78°) = cos(52° - 78°) = cos(-26°)

Now, we can use the property of even and odd functions to find the value of cos(-26°):

cos(-θ) = cos(θ) (Cosine is an even function)

So, cos(-26°) = cos(26°)

If you have the exact value of cos(26°) or a calculator to find the numerical approximation, you can get the final result.