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


2