\(\cot x=\dfrac{1}{\tan x}\)
chỗ nào có \(\cot x\) thì bạn thay bằng \(\dfrac{1}{\tan x}\)xong bấm máy như bình thường thôi.
mình ra kết quả = \(\sqrt{3}\), bạn bấm lại xem có ra giống không nhé.
\(\dfrac{tan225-cot81\cdot cot69}{cot261+tan201}\)
\(=\dfrac{tan\left(180+45\right)-tan\left(90-81\right)\cdot tan\left(90-69\right)}{cot\left(180+81\right)+tan\left(180+21\right)}\)
\(=\dfrac{tan45-tan9\cdot tan21}{cot81+tan21}\)
\(=\dfrac{1-tan9\cdot tan21}{tan9+tan21}\)
\(=\dfrac{1-\dfrac{sin9}{cos9}\cdot\dfrac{sin21}{cos21}}{\dfrac{sin9}{cos9}+\dfrac{sin21}{cos21}}\)
\(=\dfrac{cos9\cdot cos21-sin9\cdot sin21}{cos9\cdot cos21}:\dfrac{sin9\cdot cos21+sin21\cdot cos9}{cos9\cdot cos21}\)
\(=\dfrac{cos\left(9+21\right)}{cos9\cdot cos21}\cdot\dfrac{cos9\cdot cos21}{sin\left(9+21\right)}=\dfrac{cos30}{sin30}=cot30=\sqrt{3}\)
