1 General Solution of the equations of the form
(i) Sin = 0 Þ q = np , nÎI
(ii) cosq = 0 Þ q = (2n+1) (p/2) n Î I
(iii) tanq =0 Þ q = np , n Î I
(iv) sinq = 1 Þ q = 2np + (p/2)
(v) cosq = 1 Þ q = 2pn
(vi) sinq = -1 Þ q = 2np -(p/2) or 2np + (3p/2)
(vii) cosq = -1 Þ q = (2n+1) p
(viii) sinq = sina Þ q = 2p + (-1)na
(ix) cos22q = cosa Þ q = 2np ± a
(x) tanq= tana Þ q = np + a
(xi) sin2q = sin2a Þ q = np ± a
(xii) cos2q = cos2a Þ q = np ± a
(xiii) tan2q = tan2a Þ q = np ± a
2 For general solution of the equation of the form
A cosq + bsinq = c, where c £ Ö(a2+b2) , divide both side by Ö(a2+ b2)
This the equation reduces to form
now solve using above formula
3 Some important points:
(i) If while solving an equation, we have to square it, then the roots found after squaring must be checked weather they satisfy the original equation or not.
(ii)If two equation are given then find the common values of q between 0 and 2p and then 2np to this common solution (value).
|
|
