InterviewSolution
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InterviewSolution
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सिद्ध कीजिए - `2tan^(-1)((1)/(5))+sec^(-1)((5sqrt2)/(7))+2tan^(-1).(1)/(8)=(pi)/(4)` |
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Answer» L.H.S. `=2tan^(-1)((1)/(5))+sec^(-1)((5sqrt2)/(7))+2tan^(-1)((1)/(8))` `=2[tan^(-1).(1)/(5)+tan^(-1).(1)/(8)]+tan^(-1)sqrt(((5sqrt2)/(7))^(3)-1),` `" "[because sec^(-1)x=tan^(-1)sqrt(x^(2)-1)]` `=2tan^(-1)(((1)/(5)+(1)/(8))/(1-(1)/(5)xx(1)/(8)))+tan^(-1)sqrt((50)/(49)-1),` `" "[because tan^(-1)x+tan^(-1)y=tan^(-1).(x+y)/(1-xy)]` `=2tan^(-1).(13)/(39)+tan^(-1).(1)/(7)` `=2tan^(-1).(1)/(3)+tan^(-1).(1)/(7)` `=tan^(-1)((2xx(1)/(3))/(1-((1)/(3))^(2)))+tan^(-1).(1)/(7),` `" "[because 2tan^(-1)x=tan^(-1)((2x)/(1-x^(2)))]` `=tan^(-1)(((2)/(3))/((8)/(9)))+tan^(-1).(1)/(7)` `=tan^(-1)((3)/(4))+tan^(-1).(1)/(7)` `=tan^(-1)(((3)/(4)+(1)/(7))/(1-(3)/(4)xx(1)/(7)))` `=tan^(-1)((25)/(25))` `=tan^(-1)(1)` `=tan^(-1)(tan.(pi)/(4))=(pi)/(4)" "[because tan^(-1)(Tan theta)=theta]` = R.H.S. यही सिद्ध करना था। |
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