Question

Cos 7p/40*cos3p/40-sin7p/40*sin3p/40​

Answer 1

Ответ:

cos7p/40×cos3p/40-sin7p/40×sin3p/40 = cos(7p/40+3p/40)=cos10p/40=cos1p/4

Answer 2

The expression you've provided seems to be a trigonometric expression involving angles in the form of fractions. It appears to be a product of two trigonometric identities, where you're subtracting the product of sines of two angles from the product of cosines of two angles.

Let's break down the expression step by step:

1. Cosine of the Sum of Angles Identity: This identity states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B).

2. In your expression, we have A = 7π/40 and B = 3π/40. Therefore, cos(7π/40 + 3π/40) can be rewritten using the cosine of the sum of angles identity:

   cos(7π/40 + 3π/40) = cos(7π/40)cos(3π/40) - sin(7π/40)sin(3π/40)

3. You've provided an expression involving the difference of these two quantities:

   cos(7π/40)cos(3π/40) - sin(7π/40)sin(3π/40)

This is as far as we can simplify it. If you need a numerical approximation or further manipulation, you'll need to provide specific values for π (pi) and perform the calculations accordingly. Keep in mind that this expression might be used in trigonometric calculations involving angles and their trigonometric functions.