Rút gọn biểu thức P= ∝ $\frac{tan ∝ }{sin∝}$ – $\frac{sin∝}{cot∝}$ 02/09/2021 Bởi Isabelle Rút gọn biểu thức P= ∝ $\frac{tan ∝ }{sin∝}$ – $\frac{sin∝}{cot∝}$
Đáp án: $P =\cos\alpha$ Giải thích các bước giải: $\quad P =\dfrac{\tan\alpha}{\sin\alpha} – \dfrac{\sin\alpha}{\cot\alpha}$ $\to P =\dfrac{\dfrac{\sin\alpha}{\cos\alpha}}{\sin\alpha} – \dfrac{\sin\alpha}{\dfrac{\cos\alpha}{\sin\alpha}}$ $\to P =\dfrac{1}{\cos\alpha} – \dfrac{\sin^2\alpha}{\cos\alpha}$ $\to P =\dfrac{1 – \sin^2\alpha}{\cos\alpha}$ $\to P =\dfrac{\cos^2\alpha}{\cos\alpha}$ $\to P =\cos\alpha$ Bình luận
CHÚC BẠN HỌC TỐT!!! Trả lời: $P=\dfrac{\tan\alpha}{\sin\alpha}-\dfrac{\sin\alpha}{\cot\alpha}$ $=\dfrac{\dfrac{\sin\alpha}{\cos\alpha}}{\sin\alpha}-\dfrac{\sin\alpha}{\dfrac{\cos\alpha}{\sin\alpha}}$ $=\dfrac{1}{\cos\alpha}-\dfrac{\sin^2\alpha}{\cos\alpha}$ $=\dfrac{1-\sin^2\alpha}{\cos\alpha}$ $=\dfrac{\cos^2\alpha}{\cos\alpha}$ $=\cos\alpha$. Bình luận
Đáp án:
$P =\cos\alpha$
Giải thích các bước giải:
$\quad P =\dfrac{\tan\alpha}{\sin\alpha} – \dfrac{\sin\alpha}{\cot\alpha}$
$\to P =\dfrac{\dfrac{\sin\alpha}{\cos\alpha}}{\sin\alpha} – \dfrac{\sin\alpha}{\dfrac{\cos\alpha}{\sin\alpha}}$
$\to P =\dfrac{1}{\cos\alpha} – \dfrac{\sin^2\alpha}{\cos\alpha}$
$\to P =\dfrac{1 – \sin^2\alpha}{\cos\alpha}$
$\to P =\dfrac{\cos^2\alpha}{\cos\alpha}$
$\to P =\cos\alpha$
CHÚC BẠN HỌC TỐT!!!
Trả lời:
$P=\dfrac{\tan\alpha}{\sin\alpha}-\dfrac{\sin\alpha}{\cot\alpha}$
$=\dfrac{\dfrac{\sin\alpha}{\cos\alpha}}{\sin\alpha}-\dfrac{\sin\alpha}{\dfrac{\cos\alpha}{\sin\alpha}}$
$=\dfrac{1}{\cos\alpha}-\dfrac{\sin^2\alpha}{\cos\alpha}$
$=\dfrac{1-\sin^2\alpha}{\cos\alpha}$
$=\dfrac{\cos^2\alpha}{\cos\alpha}$
$=\cos\alpha$.