Question

rút gọn biểu thức:

sin a*cos a*(tan a+cot a)

Answer 1

$\sin a.\cos a.(\tan a+\cot a)\\=\sin a.\cos a.\tan a+\sin a.\cos a.\cot a\\=\sin a.\cos a.\dfrac{\sin a}{\cos a}+\sin a.\cos a.\dfrac{\cos a}{\sin a}\\=\sin^2 a+\cos^2 a\\=1$

Answer 2

\(sin\left(a\right).cos\left(a\right).\left(tan\left(a\right)+cot\left(a\right)\right)\\ =sin\left(a\right).cos\left(a\right).tan\left(a\right)+sin\left(a\right).cos\left(a\right).cot\left(a\right)\\ =sin\left(a\right).cos\left(a\right).\dfrac{sin\left(a\right)}{cos\left(a\right)}+sin\left(a\right).cos\left(a\right).\dfrac{cos\left(a\right)}{sin\left(a\right)}\\ =sin^2\left(a\right)+cos^2\left(a\right)=1\)