Question

Cos(-45 )sin 405 - cos900 / tg (-p/3)ctg (-7p/3)

Answer 1

Cos(-45°)sin(405°)-cos900°/tg(-60°)ctg(-420°)=
=cos45°.sin(360°+45°)-cos(720°+180°/tg60°ctg(360°+60°)=
=√2/2.sin45°-cos180°/√3ctg60°=(√2/2)(√2/2)-(-1)/√3.√3/3=
=2/4+1/(3/3)=1/2+1/1=1/2+1=3/2

Answer 2

Let's break down the expression step by step:

1. Cos(-45): The cosine function is periodic, and cos(-45) is equal to cos(315) since cos(-45) = cos(360 - 45). The cosine function has a value of √2/2 at 315 degrees.

2. Sin(405): The sine function is also periodic, and sin(405) is equal to sin(45) since sin(405) = sin(360 + 45). The sine function has a value of √2/2 at 45 degrees.

3. Cos(900): The cosine function is periodic, and cos(900) is equal to cos(180) since cos(900) = cos(720 + 180). The cosine function has a value of -1 at 180 degrees.

4. Tg(-π/3): The tangent function is periodic, and tg(-π/3) is equal to tg(5π/3) since tg(-π/3) = tg(-π + (-π/3)). The tangent function has a value of -√3 at 5π/3.

5. Ctg(-7π/3): The cotangent function is periodic, and ctg(-7π/3) is equal to ctg(-π/3) since ctg(-7π/3) = ctg(-6π/3 + (-π/3)). The cotangent function is the reciprocal of the tangent function, so ctg(-π/3) = -1/(-√3) = √3.

Now we can substitute the values into the expression:

cos(-45) * sin(405) - cos(900) / tg(-π/3) * ctg(-7π/3)

= (√2/2) * (√2/2) - (-1) / (-√3) * √3

= 1/2 - (-1) / (-√3) * √3

= 1/2 + 1 / √3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 + 1/√3 * √3

= 1/2 +