Câu 16 :
\(sin\left(3x-30^o\right)+cos\left(120^o-3x\right)=0\)
\(\Leftrightarrow sin\left(3x-30^o\right)+cos\left(90^o+30^o-3x\right)=0\)
\(\Leftrightarrow sin\left(3x-30^o\right)+cos\left(90^o-\left(3x-30^o\right)\right)=0\)
\(\Leftrightarrow sin\left(3x-30^o\right)+sin\left(3x-30^o\right)=0\)
\(\Leftrightarrow2sin\left(3x-30^o\right)=0\)
\(\Leftrightarrow sin\left(3x-30^o\right)=0\)
\(\Leftrightarrow3x-30^o=k180^o\left(k\in Z\right)\)
\(\Leftrightarrow x=10^o+k60^o\left(k\in Z\right)\)
Câu 17 :
\(sina+cosa=\dfrac{5}{4}\)
\(\Leftrightarrow\left(sina+cosa\right)^2=\left(\dfrac{5}{4}\right)^2\)
\(\Leftrightarrow sin^2a+cos^2a+2sinacosa=\dfrac{25}{16}\)
\(\Leftrightarrow1+2sinacosa=\dfrac{25}{16}\)
\(\Leftrightarrow sinacosa=\dfrac{1}{2}\left(\dfrac{25}{16}-1\right)=\dfrac{9}{32}\)
Chọn B
