Question

Упростить:
(tgx+ctgx)sin2x
2cos^2x/1+cos2x
2cos^2t-cos2t
Вычислить:
4sin15cos15
3sin^2a - 2sin(pi-a)+3cos^2 3a при a=pi/6

Answer 1

$(tgx+ctg x)sin2x=( frac{sin x}{cos x} + frac{cos x}{sin x} )2sin xcos x=2sin^2x+2cos^2x=2$

$frac{2cos^2x}{1+cos2x} = frac{2cos^2x}{1+2cos^2x-1} = frac{2cos^2x}{2cos^2x} =1$

$2cos^2t-cos2t=2cos^2x-2cos^2x+1=1$

$4sin15аcos15а=2sin30а=2cdot frac{1}{2} =1$

$3sin^2 alpha -2sin( pi - alpha )+3cos^23a=3sin^2 alpha -2sin alpha +3cos^23 alpha \ alpha = frac{ pi }{6} \ 3sin^2frac{ pi }{6}-2sinfrac{ pi }{6}+3cos^2frac{ pi }{2}= frac{3}{4} -1+0=- frac{1}{4}$