ધારો કે a neq 0 માટે S_a(x) = operatorname{Se | vedclass

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(C) આપેલ છે કે $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ અને $S_b(x) = \operatorname{Sec}^{-1}\left(\fra

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$ab$

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(C) આપેલ છે કે $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ અને $S_b(x) = \operatorname{Sec}^{-1}\left(\frac{x}{b}\right) + \operatorname{Sec}^{-1}(b)$.$S_a(x) = S_b(x)$ લેતા,આપણને મળે $\operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a) = \operatorname{Sec}^{-1}\left(\frac{x}{b}\right) + \operatorname{Sec}^{-1}(b)$.નિત્યસમ $\operatorname{Sec}^{-1}(y) = \cos^{-1}\left(\frac{1}{y}\right)$ નો ઉપયોગ કરતા,$\cos^{-1}\left(\frac{a}{x}\right) + \cos^{-1}\left(\frac{1}{a}\right) = \cos^{-1}\left(\frac{b}{x}\right) + \cos^{-1}\left(\frac{1}{b}\right)$.જો $x = ab$ લઈએ,તો $\cos^{-1}\left(\frac{a}{ab}\right) + \cos^{-1}\left(\frac{1}{a}\right) = \cos^{-1}\left(\frac{1}{b}\right) + \cos^{-1}\left(\frac{1}{a}\right)$.આ સમીકરણ $\cos^{-1}\left(\frac{1}{b}\right) + \cos^{-1}\left(\frac{1}{a}\right) = \cos^{-1}\left(\frac{b}{ab}\right) + \cos^{-1}\left(\frac{1}{b}\right)$ માં પરિણમે છે,જે સાચું છે.તેથી,$x = ab$ એ ઉકેલ છે.

ધારો કે $a \neq 0$ માટે $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ છે. જો $a \neq b$ માટે $S_a(x) = S_b(x)$ હોય,તો $x =$

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