InterviewSolution
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InterviewSolution
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सिद्ध कीजिए कि `cos^(-1)""((63)/(65))+2 tan^(-1)""(1)/(5))=sin^(-1)""(3)/(5)` |
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Answer» हम जानते है कि ` 2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2)))` ` 2 tan^(-1)""(1)/(5)=cos^(-1)((1-1//25)/(1+1//25))` `= cos^(-1)((24)/(26))=cos^(-1)((12)/(13))` `:.` दिये गये समीकरण से ` cos^(-1)""((63)/(65))+cos^(-1)((12)/(13))` `=cos^(-1)[(63)/(65) xx (12)/(13)-sqrt(1-((63)/(65))^(2))sqrt(1-((12)/(13))^(2))]` `= cos^(-1)[(756)/(845)-(80)/(845)]` ` =cos^(-1)[(676)/(845)]=sin^(-1)sqrt(1-((676)/(845))^(2))` `=sin^(-1)((507)/(845))` `implies cos^(-1)""(63)/(65)+cos^(-1)""(12)/(13)=sin^(-1)""(3)/(5)` |
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