InterviewSolution
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InterviewSolution
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सिद्ध कीजिए - `sin^(-1).(3)/(5)+sin^(-1).(8)/(17)=sin^(-1).(77)/(85).` |
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Answer» L.H.S. `=sin^(-1).(3)/(5)+sin^(-1).(8)/(17)` `=sin^(-1)[(3)/(5)(sqrt(1-((8)/(17))^(2)))+(8)/(1)sqrt(1-((3)/(5))^(2))]` `[because sin^(-1)x+sin^(-1)y=sin^(-1)(x sqrt(1-y^(2))+ysqrt(1-x^(2)))]` `=sin^(-1)[(3)/(5)xxsqrt((289-64)/((17)^(2)))+(8)/(17)sqrt((25-9)/((5)^(2)))]` `=sin^(-1)((3)/(5)xxsqrt((225)/(289))+(8)/(17)xxsqrt((16)/(25)))` `=sin^(-1)[(3)/(5)xx(15)/(17)+(8)/(17)xx(4)/(5)]` `=sin^(-1)((9)/(17)+(32)/(85))` `=sin^(-1)((77)/(85))` = R.H.S. यही सिद्ध करना था। |
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