Question

Cos60*sin30-sin60*cos30+cos120*tg135​

Answer 1

Ответ:

Объяснение:

формула sin(a-b)=sina*cosb-sinb*cosa

собираем первые два произведения: sin(60-30)+cos 120*tg135

по формуле приведения: sin30+cos(90+30)*tg(90+45)

sin30-sin30*(-ctg45)=sin30(1+ctg45)=1/2*(1+1)=1

Answer 2

Let's break down the expression step by step:

1. First, let's calculate the values of sin(30°) and cos(30°) and store them in variables for convenience.

   • sin(30°) = 1/2
   • cos(30°) = √3/2

2. Next, calculate the values of sin(60°) and cos(60°):

   • sin(60°) = √3/2
   • cos(60°) = 1/2

3. Calculate the value of cos(120°) by using the fact that cos(120°) = -cos(60°):

   • cos(120°) = -1/2

4. Calculate the value of tan(135°). To do this, we first find the tangent of the complementary angle (45°) and then use the identity that tan(135°) = -tan(45°):

   • tan(45°) = 1
   • tan(135°) = -1

Now, substitute these values into your expression:

Cos(60°) * Sin(30°) - Sin(60°) * Cos(30°) + Cos(120°) * Tan(135°)

= (1/2) * (1/2) - (√3/2) * (√3/2) + (-1/2) * (-1)

= 1/4 - 3/4 + 1/2

Now, combine the fractions:

= (1/4 - 3/4) + 1/2

= (-2/4) + 1/2

= -1/2 + 1/2

= 0

So, the value of the expression is 0.