Question

1) cos²105°-sin²105°
2) cos²7°+sin²7°
3) $frac{tg100 - tg70}{1+tg100*tg70}$

Answer 1

1) cos²105°-sin²105°=cos(2·105⁰)=cos210⁰=cos(180⁰+30⁰)=-cos30⁰=-√3/2
2) cos²7°+sin²7°=1( так как cos²α+sin²α=1)


$3) frac{tg100^{0}-tg70^{0}}{1+tg100^{0}*tg70^{0}} =tg(100^{0}-70^{0})=tg30^{0}= frac{ sqrt{3} }{3} \ frac{tg alpha -tg beta }{1+tg alpha *tg beta } =tg( alpha - beta )$

Answer 2

$1) cos ^{2} 105-sin^{2} 105=cos(2*105)=cos210=cos(180+30)= \ =-sin30=- frac{1}{2} =-0.5 \ 2) cos^{2} 7+sin ^{2} 7=1 \ 3) frac{tg100-tg70}{1+tg100*tg70} =tg(100-70)=tg30= frac{ sqrt{3} }{3}$