How it is solved ?

Asked by Shivendra | 23rd Jul, 2017, 10:50: AM

Expert Answer:

begin mathsize 16px style Let space straight theta equals 18 degree
Then comma space 5 straight theta equals 90 degree
rightwards double arrow 2 straight theta plus 3 straight theta equals 90 degree
rightwards double arrow 2 straight theta equals 90 degree minus 3 straight theta
rightwards double arrow sin space 2 straight theta equals sin space left parenthesis 90 degree minus 3 straight theta right parenthesis
rightwards double arrow 2 sin space straight theta space cos space straight theta equals cos space 3 straight theta
rightwards double arrow 2 sin space straight theta space cos space straight theta equals 4 cos cubed space straight theta minus 3 cos space straight theta
rightwards double arrow 2 sin space straight theta space cos space straight theta equals cos space straight theta space left parenthesis 4 cos squared space straight theta minus 3 right parenthesis
rightwards double arrow 2 sin space straight theta equals 4 cos squared space straight theta minus 3
rightwards double arrow 2 sin space straight theta minus 4 cos squared space straight theta plus 3 equals 0
rightwards double arrow 2 sin space straight theta minus 4 left parenthesis 1 minus sin squared space straight theta right parenthesis plus 3 equals 0
rightwards double arrow 2 sin space straight theta minus 4 plus 4 sin squared space straight theta plus 3 equals 0
rightwards double arrow 4 sin squared straight theta plus 2 sinθ minus 1 equals 0
Let space sin space straight theta equals straight x comma space then space we space have
4 straight x squared plus 2 straight x minus 1 equals 0
straight a equals 4 comma space straight b equals 2 comma space straight c equals negative 1
therefore space straight x equals fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction
rightwards double arrow straight x equals fraction numerator negative 2 plus-or-minus square root of 4 plus 16 end root over denominator 8 end fraction equals fraction numerator negative 2 plus-or-minus square root of 20 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
rightwards double arrow sin space straight theta equals sin space 18 degree equals fraction numerator negative 1 plus-or-minus square root of 5 over denominator 4 end fraction
SInce space sin space is space positive comma space sin space 18 degree equals fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction
Now comma space cos space 36 degree equals 1 minus 2 sin squared space 18 degree space space space space space space..... left parenthesis cos space 2 straight theta equals 1 minus 2 sin squared space straight theta right parenthesis end style

Answered by Rashmi Khot | 24th Jul, 2017, 09:34: AM