15:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 16:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 17:T5ce,

$$\begin{aligned} & \cos ^{-1}\left(\frac{y}{b}\right)=\log _e\left(\frac{x}{n}\right)^n=n \ln \left(\frac{x}{n}\right) \\ & =n \ln (x)-n \ln (n) \\ & \quad=\cos \left[\cos ^{-1}\left(\frac{y}{b}\right)\right]=\cos (n \ln x-n \ln n) \end{aligned}$$

$$\Rightarrow \frac{y}{b}=\cos (n \ln x-n \ln n)$$

$$\begin{aligned} & \Rightarrow y=b \cos (n \ln x-n \ln n) \\ & \Rightarrow y_1=-b \sin (n \ln x-n \ln n) \times \frac{n}{x} \end{aligned}$$

$$\Rightarrow y_2=-b n\left[x \times \cos (n \ln x-n \ln n) \times \frac{n}{x}\right. \left.\frac{-\sin (n \ln x-n \ln n)}{x^2}\right]$$

$$=\frac{-b n[n \cos (n \ln x-n \ln n)-\sin (n \ln x-n \ln n)]}{x^2}$$

$$\text { Now, } A y_2+B y_1+C y=0$$

$$\begin{aligned} & \Rightarrow \frac{-A b n[n \cos (n \ln x-n \ln n)-\sin (n \ln x-n \ln n)]}{x^2} \\ & -\frac{B b n \sin (n \ln x-n \ln n)}{x}+C b \cos (n \ln x-n \ln n)=0 \end{aligned}$$

$$\begin{aligned} \Rightarrow-A n^2 \cos (n \ln x-n \ln n) & +A n \sin (n \ln x \\ -n \ln n)-B n x & \sin (n \ln x-n \ln n) \\ & +C x^2 \cos (n \ln x-n \ln n)=0 \end{aligned}$$

$$\begin{aligned} \Rightarrow\left(-A n^2+C x^2\right) & \cos (n \ln x-n \ln n) +(A n-B n x) \sin (n \ln x-n \ln n)=0 \end{aligned}$$

$$\begin{aligned} & \Rightarrow \quad-A n^2+C x^2=0 \Rightarrow C x^2=A n^2 \quad \text{.... (i)}\\ & \text { and } \quad A n-B n x=0 \Rightarrow A=B x \quad \text{.... (ii)}\\ & \therefore \quad A=x^2, B=x, C=n^2 \end{aligned}$$

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