Question

Cos135 -sin240+cos315+sin120;

Answer 1

Cos 135=(90+45)= корень квадратный из двух на 2

Answer 2

Let's break down each term and simplify:

cos(135) = cos(90 + 45) = -sin(45) = -sqrt(2)/2

sin(240) = sin(180 + 60) = -sin(60) = -sqrt(3)/2

cos(315) = cos(270 + 45) = -sin(45) = -sqrt(2)/2

sin(120) = sin(90 + 30) = cos(30) = sqrt(3)/2

Putting it all together:

cos135 - sin240 + cos315 + sin120 = (-sqrt(2)/2) - (-sqrt(3)/2) - (sqrt(2)/2) + (sqrt(3)/2)

Simplifying the terms:

= -sqrt(2)/2 + sqrt(2)/2 - sqrt(3)/2 + sqrt(3)/2

= 0

Therefore, the expression evaluates to 0.