Other Math Archive: Questions from September 16, 2023
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Prove the following trigonometric identities: (a) \( \ln (\sec y+\tan y)+\ln (\sec y-\tan y)=0 \) (b) \( \frac{\tan x}{\sec x-1}=\frac{\sec x+1}{\tan x} \) (c) \( \frac{\cos 2 \theta}{1+\sin 2 \theta}1 answer -
2. Find all solutions for the ODEs, and if available A. \( y^{\prime}=-\cos x \) B. \( y^{\prime}=x \ln x \) C. \( y^{\prime \prime}=2 x+\sin x+e^{x} \)1 answer -
(1) \( y=\sin ^{-1}\left(\frac{x^{2}+6}{x^{2}}\right. \) (2) \( y=\tan ^{-1}\left(\frac{x^{2}}{6+2 x^{3}}\right) \)0 answers -
Sketch each set of functions on the same set of axes. a) \( y=x^{2}, y=3 x^{2}, y=3(x-2)^{2}+1 \) b) \( y=\sqrt{x}, y=\sqrt{3 x}, y=\sqrt{-3 x}, y=\sqrt{-3(x+1)}-4 \) c) \( y=\frac{1}{x}, y=\frac{2}{x1 answer