Toán Lớp 9: a) tính Sinx, cosx nếu biết x nhọn và tanx=12/35 b) cho góc alpha nhọn và cosa=5/13. Tính sina, tana,cota

a/ $\tan x=\dfrac{12}{35}\\↔\dfrac{\sin x}{\cos x}=\dfrac{12}{35}\\↔\sin x=\dfrac{12\cos x}{35}\\\sin ^2 x+\cos^2 x=1\\↔\left(\dfrac{12\cos x}{35}\right)^2+\cos^x =1\\↔\dfrac{144\cos^2 x}{1225}+\cos^2 x=1\\↔\dfrac{1369\cos ^2 x}{1225}=1\\↔\cos^2 x=\dfrac{1225}{1369}\\↔\cos x=\dfrac{35}{37}(x>0)\\→\sin x=\dfrac{12}{37}$

Vậy $\sin x=\dfrac{12}{37},\cos x=\dfrac{35}{37}$

b/ $\cos\alpha=\dfrac{5}{13}\\↔\cos^2\alpha=\dfrac{25}{169}\\\cos^2\alpha+\sin^2\alpha=1\\↔\dfrac{25}{169}+\sin^2\\alpha=1\\↔\sin^2\alpha=\dfrac{144}{169}\\↔\sin\alpha=\dfrac{12}{13}(\alpha>0)\\\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}\\↔\tan\alpha=\dfrac{12}{5}\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\↔\cot\alpha=\dfrac{5}{12}$

Vậy $\sin\alpha=\dfrac{12}{13},\tan\alpha=\dfrac{12}{5},\cot\alpha=\dfrac{5}{12}$