Question

Вычислите 6sin15°cos15°/2cos^2 15° -1

Answer 1

=3sin30/cos30=3*tg30=3*1/√3=3/√3=√3

Answer 2

$cos2a=cos^2a-sin^2a=cos^2a-(1-cos^2a)=2cos^2a-1\\Esli; a=15^0,; to; 2cos^215^0-1=cos30^0\\2sinacdot cosa=sin2a\\Esli; a=15^0,to; 2sin15^0cos15^0=sin30^0\\frac{6sin15^0cos15^0}{2cos^215^0-1}=frac{3sin30^0}{cos30^0}=3tg30^0=3cdot frac{sqrt3}{3}=sqrt3$