InterviewSolution
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InterviewSolution
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ज्ञात करें : `tan[(1)/(2) cos^(-1)""(sqrt(5))/(3)]` |
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Answer» माना कि `cos^(-1)((sqrt(5))/(2))= 2theta` तो `cos 2theta = (sqrt(5))/(3)` तथा `0 le 2theta le pi` अब, `cos 2theta = (sqrt(5))/(3)` `therefore (1-tan^(2)theta)/(1+tan^(2)theta) = (sqrt(5))/(3)` या, `(1+tan^(2)theta)/(1-tan^(2)theta) = (3)/(sqrt(5))` या, `(2tan^(2)theta)/(2) = (3-sqrt(5))/(3+sqrt(5)) " "` [योगान्तर निष्पत्ति से] या, `tan^(2) = ((3-sqrt(5))/(3+sqrt(5)))((3-sqrt(5))/(3-sqrt(5)))" "...(i)` लेकिन `0 le 2theta le pi " " therefore le theta le (pi)/(2)` `rArr theta` पहले पाद में है | अतः `tan theta` धन होगा | `therefore` (1) से, `tan theta = (3-sqrt(5))/(2)` |
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