Question

Sin(90°-α) - cos(180°-α) + tg(180°-α)-ctg(270°+α)

Answer 1

Ответ:

2cosα

Объяснение:

$\sin(90 - \alpha ) - \cos(180 - \alpha ) + \tan(180 - \alpha ) - \cot(270 + \alpha ) = \\ = \cos( \alpha ) + \cos( \alpha ) + \tan( \alpha ) - \tan( \alpha ) = 2 \cos( \alpha )$

Answer 2

Let's simplify the expression step by step:

1. sin(90°-α):

   • Since sin(90°) = 1, we have sin(90°-α) = sin(90°)cos(α) - cos(90°)sin(α) = cos(α).

2. cos(180°-α):

   • Since cos(180°) = -1, we have cos(180°-α) = cos(180°)cos(α) + sin(180°)sin(α) = -cos(α).

3. tan(180°-α):

   • Since tan(180°) is undefined, we have tan(180°-α) = tan(180°) = 0.

4. cot(270°+α):

   • Since cot(270°) is undefined, we have cot(270°+α) = cot(270°) = 0.

Now, let's put it all together:

cos(α) - (-cos(α)) + 0 - 0

= cos(α) + cos(α)

= 2cos(α)

So, the simplified expression is 2cos(α).