Question

Упростить выражение 1 )Sin 2t/cos t + sin t, 2) sin ²t+ cos 2t, 3) sin 2t/ cos t, 4) cos 2t/ cost- sin t буду благодарен если с развернутыми ответами

Answer 1

1) $\displaystyle \frac{sin (2t)}{cos(t)}+ sin t=\frac{2*sin(t)*cos(t)}{cos(t)}+ sin t=2sin(t)+ sin t = 3sin t$

2) $\displaystyle sin ^{2}(t)+ cos (2t)=sin ^{2}(t)+(cos ^{2}(t)-sin ^{2}(t))=sin ^{2}(t)+cos ^{2}(t)-sin ^{2}(t)=$

$\displaystyle = cos^{2}(t)$

3) $\displaystyle \frac{sin(2t)}{cos(t)} = \frac{2*sin(t)*cos(t)}{cos(t)}=2sin(t)$

4) $\displaystyle \frac{cos(2t)}{cos(t)-sin(t)} =\frac{cos^{2}(t)-sin^{2}(t)}{cos(t)-sin(t)} =\frac{(cos(t)-sin(t))(cos(t)+sin(t))}{cos(t)-sin(t)}=$

$\displaystyle =cos(t)+sin(t)$