cho tana = 2 . Giá trị của biểu thức A = $\frac{sina}{sin^{3}a+2cos^{3}a }$ 04/08/2021 Bởi Camila cho tana = 2 . Giá trị của biểu thức A = $\frac{sina}{sin^{3}a+2cos^{3}a }$
CHÚC BẠN HỌC TỐT!!! Trả lời: $\tan a=2⇒\cot a=\dfrac{1}{2}$ $A=\dfrac{\sin a}{\sin^3 a+2\cos^3a}=\dfrac{\dfrac{\sin a}{\sin a}}{\dfrac{\sin^3a}{\sin a}+3.\dfrac{\cos^3a}{\sin a}}\\\,\,\,\,\,=\dfrac{1}{\sin^2a+2.\cot a.\cos^2a}=\dfrac{1}{\sin^2a+2\dfrac{1}{2}.\cos^2a}\\\,\,\,\,\,=\dfrac{1}{\sin^2a+\cos^2a}=\dfrac{1}{1}=1.$ Bình luận
$A=\dfrac{\sin \alpha}{\sin^3 \alpha+2\cos^3 \alpha}=\dfrac{\dfrac{\sin \alpha}{\cos^3 \alpha}}{\dfrac{\sin^3 \alpha+2\cos^3 \alpha}{\cos^3 \alpha}}$ $=\dfrac{\tan \alpha . \dfrac1{\cos^2 \alpha}}{\tan^3 \alpha +2}=\dfrac{\tan \alpha \big(1+\tan^2 \alpha\big)}{\tan^3 \alpha+2}$ $=\dfrac{2\big(1+2^2\big)}{2^3+2}=\dfrac{10}{10}=1$ Bình luận
CHÚC BẠN HỌC TỐT!!!
Trả lời:
$\tan a=2⇒\cot a=\dfrac{1}{2}$
$A=\dfrac{\sin a}{\sin^3 a+2\cos^3a}=\dfrac{\dfrac{\sin a}{\sin a}}{\dfrac{\sin^3a}{\sin a}+3.\dfrac{\cos^3a}{\sin a}}\\\,\,\,\,\,=\dfrac{1}{\sin^2a+2.\cot a.\cos^2a}=\dfrac{1}{\sin^2a+2\dfrac{1}{2}.\cos^2a}\\\,\,\,\,\,=\dfrac{1}{\sin^2a+\cos^2a}=\dfrac{1}{1}=1.$
$A=\dfrac{\sin \alpha}{\sin^3 \alpha+2\cos^3 \alpha}=\dfrac{\dfrac{\sin \alpha}{\cos^3 \alpha}}{\dfrac{\sin^3 \alpha+2\cos^3 \alpha}{\cos^3 \alpha}}$
$=\dfrac{\tan \alpha . \dfrac1{\cos^2 \alpha}}{\tan^3 \alpha +2}=\dfrac{\tan \alpha \big(1+\tan^2 \alpha\big)}{\tan^3 \alpha+2}$
$=\dfrac{2\big(1+2^2\big)}{2^3+2}=\dfrac{10}{10}=1$