निम्नलिखित समीकरण को हल कीजिए - `sec^(-1)((x)/(a))-sec^(-1)((x)/(b))=sec^(-1)(b)-sec^(-1)(a).`

निम्नलिखित समीकरण को हल की

1.	निम्नलिखित समीकरण को हल कीजिए - `sec^(-1)((x)/(a))-sec^(-1)((x)/(b))=sec^(-1)(b)-sec^(-1)(a).`
Answer» दिया गया समीकरण है - `sec^(-1)((x)/(a))-sec^(-1)((x)/(b))=sec^(-1)(b)-sec^(-1)(a)` `rArr cos^(-1)((a)/(x))-cos^(-1)((b)/(x))=cos^(-1)((1)/(b))-cos^(-1)((1)/(a))," "[because sec^(-1)x=cos^(-1)((1)/(x))]` `rArr cos^(-1)((a)/(x))+cos^(-1)((1)/(a))=cos^(-1)((1)/(b))+cos^(-1)((b)/(x))` `rArr cos^(-1)[(a)/(x).(1)/(a)-sqrt(1-(a^(2))/(x^(2)))sqrt(1-(1)/(a^(2)))]` `" "=cos^(-1)[(1)/(b).(b)/(x)-sqrt(1-(1)/(b^(2)))sqrt(1-(b^(2))/(x^(2)))]` `rArr cos^(-1)[(1)/(x)-sqrt((x^(2)-a^(2))/(x^(2)))sqrt((a^(2)-1)/(a^(2)))]` `=cos^(-1)[(1)/(x)-sqrt((b^(2)-1)/(b^(2)))sqrt((x^(2)-b^(2))/(x^(2)))]` `rArr (1)/(x)-sqrt((x^(2)-a^(2))/(x^(2)))sqrt((a^(2)-1)/(a^(2)))` `rArr sqrt((x^(2)-a^(2))/(x^(2)))sqrt((a^(2)-1)/(a^(2)))=sqrt((b^(2)-1)/(b^(2)))sqrt((x^(2)-b^(2))/(b^(2)))` `rArr ((x^(2)-a^(2))(a^(2)-1))/(a^(2)x^(2))=((x^(2)-b^(2))(b^(2)-1))/(b^(2)x^(2)),`