Question

Sin (180 - d ) cos (270 + d) * tg (90 + d)

Answer 1

Ответ:     - ( 1/2 )sin2α .

Пошаговое объяснение:

sin (180° - α ) cos (270° + α ) * tg (90° + α ) = +sinα * ( + sinα )*( - ctgα ) =

= - sin²α * ( cosα/sinα ) = - sinα cosα = - (1/2)*2sinα cosα = - ( 1/2 )sin2α .

Answer 2

Let's break down the expression step by step:

1. sin(180 - d): This is the sine of the angle (180 - d) degrees. Since the sine function has a periodicity of 360 degrees, you can simplify this to -sin(d) because sin(180 - d) = -sin(d).

2. cos(270 + d): This is the cosine of the angle (270 + d) degrees. Cosine is also periodic every 360 degrees, so you can simplify this to cos(d) because cos(270 + d) = cos(d).

3. tan(90 + d): This is the tangent of the angle (90 + d) degrees. Tangent is periodic every 180 degrees, so you can simplify this to tan(d) because tan(90 + d) = tan(d).

Now, you have:

• -sin(d) * cos(d) * tan(d)

To further simplify, you can use the fact that -sin(d) * cos(d) = -sin(2d):

• -sin(2d) * tan(d)

So, the expression can be simplified to:

-sin(2d) * tan(d)