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