Cos65°cos5°+sin5°cos25°

Предыдущий
вопрос Следующий
вопрос

= cos(65°)cos(5°) + sin(5°)cos(25°)

Using the trigonometric identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b), we can rewrite this expression as:

cos(65°)cos(5°) + sin(5°)cos(25°)
= cos(60° + 5°)cos(5°) + sin(5°)cos(25°)
= [cos(60°)cos(5°) - sin(60°)sin(5°)]cos(5°) + sin(5°)cos(25°)
= [(1/2)(cos(5°)) - (√3/2)(sin(5°))]cos(5°) + sin(5°)cos(25°)
= (1/2)cos²(5°) - (√3/2)sin(5°)cos(5°) + sin(5°)cos(25°)

Given that sin(2θ) = 2sin(θ)cos(θ), we can simplify further:

= (1/2)cos²(5°) - (√3/2)(1/2)sin(10°) + sin(5°)cos(25°)
= (1/2)cos²(5°) - (√3/4)sin(10°) + sin(5°)cos(25°)