Question

помогите решить 
1)1-(cos²$alpha$ - sin²$alpha$ ) =?
2)1-sin$alpha$cos$alpha$tg$alpha$ =?
3) cos²$alpha$tg²$alpha$ + 5cos²$alpha$ - 1=?
4) sin$alpha$ + 3sin²$alpha$ + 3cos²$alpha$ =?

Answer 1

$1)1-(cos^2 alpha - sin^2 alpha ) =cos^ alpha +sin^2 alpha -cos^2 alpha +sin^2 alpha =2sin^2 alpha$

$2)1-sin alphacdot cos alpha cdot tg alpha =1-sin alpha cdot cos alpha cdot frac{sin alpha }{cos alpha }=1-sin^2 alpha =cos^2 alpha$

$3) cos^2alphacdot tg^2 alpha + 5cos^2 alpha - 1= \ \=cos^2alphacdot frac{sin^2 alpha}{cos^2 alpha} + 5cos^2 alpha - 1=sin alpha ^{2}+cos^2 alpha +4cos^2 alpha -1=\ \==1+4cos^2 alpha-1=4cos^2 alpha$

$4) sin alpha + 3sin^2 alpha+3cos^2 alpha =sin alpha +3(sin^2 alpha +cos^2 alpha )=sin alpha +3cdot1= \ \ =sin alpha +1$