Question

Cos^2(90+a) + cos^2(180-a) + tg (270-a)×tg(180+a)

Answer 1

Cos²(90° + α) + Cos²(180° - α) + tg(270° -α) * tg(180° + α) =

= Sin²α + Cos²α + Ctgα * Tgα = (Sin²α + Cos²α) + (Ctgα * Tgα) = 1 + 1 = 2

Answer 2

Let's break down each part of the expression step by step:

1. cos^2(90 + a): The cosine function has a period of 360 degrees, and cos(90 degrees) = 0. Therefore, cos^2(90 + a) = 0 for any value of 'a'.

2. cos^2(180 - a): Similarly, the cosine function has a period of 360 degrees, and cos(180 degrees) = -1. Therefore, cos^2(180 - a) = (-1)^2 = 1 for any value of 'a'.

3. tan(270 - a): The tangent function has a period of 180 degrees, and tan(270 degrees) is undefined (because it's at the vertical asymptote of the tangent function). So, tan(270 - a) is also undefined for any value of 'a'.

4. tan(180 + a): The tangent function has a period of 180 degrees, and tan(180 degrees) = 0. Therefore, tan(180 + a) = tan(a) for any value of 'a'.

Now, combining all the results:

cos^2(90 + a) + cos^2(180 - a) + tan(270 - a) * tan(180 + a) = 0 + 1 + (undefined) * tan(a) = 1 + (undefined) * tan(a)

So, the expression simplifies to 1 + (undefined) * tan(a). Since tan(270 - a) is undefined for any value of 'a', the final result is 1 + (undefined). In mathematical terms, this expression is undefined.