Toán (1 + sin α)(1 − sin α) = cot^2 ( pi/4 – α/2 ). Giúp e với ạ !!! 17/10/2021 By Jasmine (1 + sin α)(1 − sin α) = cot^2 ( pi/4 – α/2 ). Giúp e với ạ !!!
Giải thích các bước giải: $VP=\cot^2\left ( \dfrac{\pi}{4}-\dfrac{\alpha}{2} \right )\\=\dfrac{1}{\sin^2\left ( \dfrac{\pi}{4}-\dfrac{\alpha}{2} \right )}-1\\=\dfrac{2}{1-\cos\left ( 2.\dfrac{\pi}{4}-2.\dfrac{\alpha}{2} \right )}-1\\=\dfrac{2}{1-\cos\left ( \dfrac{\pi}{2}-\alpha \right )}-1\\=\dfrac{2}{1-\sin\alpha}-1\\=\dfrac{2}{1-\sin\alpha}-\dfrac{1-\sin\alpha}{1-\sin\alpha}\\=\dfrac{2-1+\sin\alpha}{1-\sin\alpha}\\=\dfrac{1+\sin\alpha}{1-\sin\alpha}=VT\Rightarrow đpcm$ Trả lời
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Giải thích các bước giải:
$VP=\cot^2\left ( \dfrac{\pi}{4}-\dfrac{\alpha}{2} \right )\\
=\dfrac{1}{\sin^2\left ( \dfrac{\pi}{4}-\dfrac{\alpha}{2} \right )}-1\\
=\dfrac{2}{1-\cos\left ( 2.\dfrac{\pi}{4}-2.\dfrac{\alpha}{2} \right )}-1\\
=\dfrac{2}{1-\cos\left ( \dfrac{\pi}{2}-\alpha \right )}-1\\
=\dfrac{2}{1-\sin\alpha}-1\\
=\dfrac{2}{1-\sin\alpha}-\dfrac{1-\sin\alpha}{1-\sin\alpha}\\
=\dfrac{2-1+\sin\alpha}{1-\sin\alpha}\\
=\dfrac{1+\sin\alpha}{1-\sin\alpha}=VT\Rightarrow đpcm$