Find the general solution of each of the following equations:
(i)
(ii)
(iii) tan x = -1
To Find: General solution.
(i) Given: cos x =
Formula used: cos = cos = 2n , n I
By using above formula, we have
cos x = = cos()= cos()=cos() x = 2n , n I
So general solution is x = 2n where n I
(ii) Given: cosec x =
We know that cosec sin = 1
So sinx =
Formula used: sin = sin = n + (-1)n , n
By using above formula, we have
sinx = = sin x = n +(-1)n.
So general solution is x = n +(-1)n. where n I
(iii) Given: tan x = -1
Formula used: tan = tan = n , n I
By using above formula, we have
tan x = -1= tan x = n, n I
So the general solution is x = nwhere n I