Find the general solution of each of the following equations:
(i) sec 3x = -2
(ii) cot 4x = -1
(iii)
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