Question

Sin2(П-а)+cos2(2П-а)-ctg(П/2-а)×ctg(П+а)=?

Answer 1

=sin(a)+cos(a)-tg(a)*ctg(a)=sin(a)=cos(a)-tg(a)*1/tg(a) (котангенс расписали) = sin(a)+cos(a)-1

Answer 2

To simplify the given expression, we'll use trigonometric identities. Let's break it down step by step:

1. Sin^2(π - a) = sin^2(a) (using the identity: sin(π - x) = sin(x))

2. Cos^2(2π - a) = cos^2(a) (using the identity: cos(2π - x) = cos(x))

3. Ctg(π/2 - a) = 1 / tan(π/2 - a) = 1 / cot(a) = tan(a) (using the identity: cot(x) = 1 / tan(x))

4. Ctg(π + a) = -cot(a) (using the identity: cot(x + π) = -cot(x))

Now, let's rewrite the expression with these substitutions:

sin^2(a) + cos^2(a) - tan(a) * (-cot(a))

Since sin^2(a) + cos^2(a) = 1 (using the Pythagorean identity for sine and cosine), the expression simplifies to:

1 + tan(a) * cot(a)

Now, remember that tan(a) * cot(a) = 1, so the final answer is:

1 + 1 = 2