InterviewSolution
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InterviewSolution
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सिद्ध कीजिए - `sin^(-1).(4)/(5)+sin^(-1).(5)/(13)+sin^(-1).(16)/(65)=(pi)/(2).` |
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Answer» L.H.S. `=sin^(-1).(4)/(5)+sin^(-1).(5)/(13)+sin^(-1).(16)/(65)` `=sin^(-1)[(4)/(5)xxsqrt(1-((5)/(13))^(2))+(5)/(13)xxsqrt(1-((4)/(5))^(2))]+sin^(-1).(16)/(65)` `=sin^(-1)[(4)/(5)xxsqrt((144)/(169))+(5)/(13)xx sqrt((9)/(25))]+sin^(-1).(16)/(65)` `=sin^(-1)((4)/(5)xx(12)/(13)+(5)/(13)xx(3)/(5))+sin^(-1).(16)/(65)` `=sin^(-1)((45)/(65)+(15)/(65))+sin^(-1).(16)/(65)` `=sin^(-1)((63)/(65))+sin^(-1)((16)/(65))` `=sin^(-1)[(63)/(65)sqrt(1-((16)/(65))^(2))+(16)/(65)sqrt(1-((63)/(65))^(2))]` `=sin^(-1)[(63)/(65)sqrt((4225-256)/(4225))+(16)/(65)xxsqrt((4225-3969)/(4225))]` `=sin^(-1)[(63)/(65)xxsqrt((3969)/(4225))+(16)/(65)xx sqrt((256)/(4225))]` `=sin^(-1)[(63)/(65)xx(63)/(65)+(16)/(65)xx(16)/(65)]` `=sin^(-1)((3969+256)/(4225))` `=sin^(-1)((4225)/(4225))` `=sin^(-1)=(pi)/(2)` = R.H.S. यही सिद्ध करना था। |
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