InterviewSolution
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InterviewSolution
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In each of the following , find the general value of x satisfying the equation : (i) `sinx =(-sqrt(3))/(2)` (ii) `cosx=(-1)/(2)` (iii) `cotx=-sqrt(3)` |
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Answer» (i) `sinx=(-sqrt(3))/(2)=-"sin"(pi)/(3)= sin(pi+(pi)/(3))="sin"(4pi)/(3)`. `thereforesinx " sin"(4pi)/(3)rArrx={npi+(-1)^(n)*(4pi)/(3))`, where `n in I`. Hence , the general solution is x = `{npi+(-1)^(n)*(4pi)/(3))`, where `ninI`. (ii) `cosx=(-1)/(2)=-"cos "(pi)/(3)=cos(pi-(pi)/(3))="cos "(2pi)/(3)`. `therefore cos x="cos"(2pi)/(3)rArrx=(2npi+-(2pi)/(3))` , where `ninI`. Hence , the general solution is x `=(2npi+-(2pi)/(3))` , where `nin I`. (iii) `cotx=-sqrt(3)` `rArrtanx =(-1)/(sqrt(3))=-"tan"(pi)/(6)="tan"(pi-(pi)/(6))="tan"(5pi)/(6)` `rArr"tan " x = "tan " (5pi)/(6)` `rArrx=(npi+(5pi)/(6))`, where `ninI`. |
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