Q. 7

Find the general solution of each of the following equations:

(i) sec 3x = -2

(ii) cot 4x = -1

(iii)

Answer :

To Find: General solution.


(i) Given: sec 3x = -2


We know that sec cos = 1


So cos 3x =


Formula used: cos = cos = 2n , n I


By using above formula, we have


cos 3x = = -cos= cos= cos 3x = 2n x = , n I


So the general solution is x = , ,where n I


(ii) Given: cot 4x = -1


We know that tan cot = 1


So tan 4x = -1


Formula used: tan = tan = n , n I


By using above formula, we have


tan 4x = -1= tan 4x = n x = , n I


So general solution is x = (4n+3) ,where n I


(iii) Given: cosec 3x =


We know that cosec sin = 1


So sin 3x =


Formula used: sin = sin = n + (-1)n. , n I


By using above formula, we have


sin 3x = = sin 3x= n +(-1)n . x= +(-1)n . , n I


So general solution is x = +(-1)n . , where n I


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