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= pi/4+pin

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

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

x = \frac{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{π}{4} + πn

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

Combine all the solutions

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn

x = \frac{π}{4} + πn

\frac{1}{cos ( 2 x )} + tan (2 x) = 3 cos (2 x), 0^{\circ} < x < 9 0^{\circ}

sin (x) = \frac{4}{5}, 0 \leq x < 2 π

7 sin^{2} (θ) - 5 sin (θ) = 2

sec (2 x) = - (\frac{2}{3})

\frac{e ^{- l n (- \frac{s i n ( θ )}{c o s ( θ )})}}{2} \cdot sin (θ) = 0

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= pi/4+pin