Find the general solution of each of the following equations:
(i) sin 3x = 0
(ii)
(iii)
(iv) cos 2x = 0
(v)
(vi)
(vii) tan 2x = 0
(viii)
(ix)
To Find: General solution.
[NOTE: A solution of a trigonometry equation generalized by means of periodicity, is known as general solution]
(i) Given: sin 3x = 0
Formula used: sin= 0 = n , n I
By using above formula, we have
sin 3x = 0 3x = n x = where n I
So general solution is x= where n I
(ii) Given: sin = 0
Formula used: sin= 0 = n , n I
By using above formula, we have
sin = 0 = n x = where n I
So general solution is x= where n I
(iii) Given: sin = 0
Formula used: sin= 0 = n , n I
By using the above formula, we have
sin = 0 = n x = n- where n I
So general solution is x= n- where n I
(iv) Given: cos 2x = 0
Formula used: cos= 0 = (2n+1) , n I
By using above formula, we have
cos 2x = 0 2x = (2n+1) x = (2n+1) where n I
So general solution is x= (2n+1)where n I
(v) Given: cos = 0
Formula used: cos= 0 = (2n+1) , n I
By using the above formula, we have
cos = 0 = (2n+1) x = (2n+1) where n I
So general solution is x= (2n+1)where n I
(vi) Given: cos = 0
Formula used: cos= 0 = (2n+1) , n I
By using the above formula, we have
cos = 0 = (2n+1) x = (2n+1) - x = n + where n I
So general solution is x= n + where n I
(vii) Given: tan 2x = 0
Formula used: tan= 0 = n , n I
By using above formula, we have
tan 2x = 0 2x = n x = where n I
So general solution is x= where n I
(viii) Given: tan = 0
Formula used: tan= 0 = n , n I
By using above formula, we have
tan = 0 = n 3x = n - x = - where n I
So general solution is x = - where n I
(ix) Given: tan = 0
Formula used: tan= 0 = n , n I
By using above formula, we have
tan = 0 = n 2x = n - x = + where n I
So general solution is x = + where n I