Question

Помогите упростить выражения:
1. 1-cos^2a + sin^2a
2. sina / 1+cosa + 1+cosa/sina
3. (1/cos^2a-1) ctg^2a
4. sin^3a + cos^3a/ 1-sina cosa - cosa) ctga

Answer 1

$1. 1-cos^2a + sin^2a=sin^2a+sin^2a=2sin^2a\ \ \ 2. frac{sina}{1+cosa}+frac{1+cosa}{sina} =frac{sin^2a+1+2cosa+cos^2a}{(1+cosa)sina}=frac{1+1+2cosa}{(1+cosa)*sina}=frac{2(1+cosa)}{(1+cosa)*sina}=frac{2}{sina} \ \ \ 3. (frac{1}{cos^2a}-1 )ctg^2a=frac{1-cos^2a}{cos^2a}*ctg^2a=frac{sin^2a}{cos^2a}*frac{cos^2a}{sin^2a}$

$4. (frac{sin^3a + cos^3a}{1-sina cosa} -cosa)*ctga=(frac{(sina+cosa)(sin^2a-cosa*sina+sin^2a)}{1-sina*cosa} -cosa)*ctga=\ \(frac{(sina+cosa)(1-cosa*sina)}{1-sina*cosa} -cosa)*ctga=(sina+cosa-cosa)*ctga=\ \ sina*frac{cosa}{sina}=cosa$