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CBSE Class 11-science Answered

find the value of sin18 degree???
Asked by Ravikant | 16 Feb, 2016, 07:04: PM
answered-by-expert Expert Answer
begin mathsize 11px style Let space straight theta equals 18 degree rightwards double arrow 90 degree equals 2 cross times 18 degree plus 3 cross times 18 degree rightwards double arrow 90 degree equals 2 straight theta plus 3 straight theta rightwards double arrow 3 straight theta equals 90 degree minus 2 straight theta rightwards double arrow sin 3 straight theta equals sin open parentheses 90 degree minus 2 straight theta close parentheses rightwards double arrow 3 sinθ minus 4 sin cubed straight theta equals cos 2 straight theta rightwards double arrow 3 sinθ minus 4 sin cubed straight theta equals 1 minus 2 sin squared straight theta Substitute space sinθ equals straight t The space equation space becomes space 4 straight t cubed minus 2 straight t squared minus 3 straight t plus 1 equals 0 By space inspection comma space straight t equals 1 space is space straight a space solution space of space the space above space equation. So space dividing space space 4 straight t cubed minus 2 straight t squared minus 3 straight t plus 1 space by space open parentheses straight t minus 1 close parentheses comma space we space get space 4 straight t squared plus 2 straight t minus 1 Hence comma space 4 straight t cubed minus 2 straight t squared minus 3 straight t plus 1 equals open parentheses straight t minus 1 close parentheses open parentheses 4 straight t squared plus 2 straight t minus 1 close parentheses Since space straight t not equal to 1 space left parenthesis sin space 18 space has space to space be space less space than space 1 right parenthesis comma 4 straight t cubed minus 2 straight t squared minus 3 straight t plus 1 equals 0 rightwards double arrow 4 straight t squared plus 2 straight t minus 1 equals 0 rightwards double arrow straight t equals fraction numerator negative 2 plus-or-minus square root of 2 squared plus 16 end root over denominator 8 end fraction equals fraction numerator negative 2 plus-or-minus 2 square root of 5 over denominator 8 end fraction equals fraction numerator negative 1 plus-or-minus square root of 5 over denominator 4 end fraction Hence comma space straight t equals sin 18 degree equals fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction space left parenthesis taking space the space positve space value space as space sinθ greater than 0 space for space 0 degree less than straight theta less than 90 degree right parenthesis end style
Answered by satyajit samal | 17 Feb, 2016, 11:21: AM

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