What is the general solution for (tan(x)+1)(sin(x)-1)=0 ?

The general solution for (tan(x)+1)(sin(x)-1)=0 is x=(3pi)/4+pin

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(tan(x)+1)(sin(x)-1)=0

(tan (x) + 1) (sin (x) - 1) = 0

x = \frac{3 π}{4} + πn

Solution steps

(tan (x) + 1) (sin (x) - 1) = 0

Solving each part separately

tan (x) + 1 = 0 or sin (x) - 1 = 0

tan (x) + 1 = 0 : x = \frac{3 π}{4} + πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

x = \frac{3 π}{4} + πn

5 cos (a) + 8 = 3 cos (a) + 6

cos (x) = \frac{- 3}{4}

3 cot^{2} (x) - 9 = 0

\frac{2}{5} = cos (θ)

2 - 2 cos^{2} (x) = sin (x)

What is the general solution for (tan(x)+1)(sin(x)-1)=0 ?
The general solution for (tan(x)+1)(sin(x)-1)=0 is x=(3pi)/4+pin