Toán Lớp 10: Chứng minh rằng 1+Sin² a/ 1-Sin² a =1+2tan² a -

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Toán Lớp 10: Chứng minh rằng 1+Sin² a/ 1-Sin² a =1+2tan² a

Thảo Tháng Bảy 7, 2022 Toán học 1 Comment 0 views

Toán Lớp 10: Chứng minh rằng
1+Sin² a/ 1-Sin² a =1+2tan² a

Comments ( 1 )

hienchaudiem
7 Tháng Bảy, 2022 at 11:36 sáng

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~rai~

\(\dfrac{1+\sin^2\alpha}{1-\sin^2\alpha}=1+2\tan^2\alpha\\\text{Xét VT=}\dfrac{1+\sin^2\alpha}{1-\sin^2\alpha}\\\quad\quad\quad=\dfrac{\cos^2\alpha+\sin^2\alpha+\sin^2\alpha}{\cos^2\alpha}\\\quad\quad\quad=\dfrac{\cos^2\alpha+2\sin^2\alpha}{\cos^2\alpha}\\\quad\quad\quad=\dfrac{\cos^2\alpha}{\cos^2\alpha}+\dfrac{2\sin^2\alpha}{\cos^2\alpha}\\\quad\quad\quad=1+2\tan^2\alpha\\\quad\quad\quad=VP.\\\Rightarrow \dfrac{1+\sin^2\alpha}{1-\sin^2\alpha}=1+2\tan^2\alpha.(đpcm)\\\text{Công thức áp dụng:}\\+)\sin^2\alpha+\cos^2\alpha=1.\\+)\dfrac{\sin\alpha}{\cos\alpha}=\tan\alpha.\)

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