Question

упростить выражение:
а)sint*cost*tgt=
б)sint*cost*ctgt-1=
в)sinквt -tgt* ctgt=
г) 1-cosквt/ 1-sinкв t=

Answer 1

$sint*cost*tgt=sint*cost* frac{sint}{cost}=sin^2t\\sint*cost*ctgt-1=\=sint*cost* frac{cost}{sint}-1=cos^2t-1=cos^2t-cos^2-sin^2t=-sin^2t\\sin^2t-tgt*ctgt=sin^2t-1=sin^2t-sin^2t-cos^2t=-cos^2t\\ frac{1-cos^2t}{1-sin^2t}= frac{sin^2t}{cos^2t}=tg^2t$