determine the general solution of: tanxsinx + cosxtanx =0
asked by guest
You asked:
Solve the equation
tan ( x ) sin ( x ) + cos ( x ) tan ( x ) = 0 \tan\left( x \right) \sin\left( x \right) + \cos\left( x \right) \tan\left( x \right) = 0 tan ( x ) sin ( x ) + cos ( x ) tan ( x ) = 0 for the variable
x x x .
MathBot Answer:
The real solutions are: x = { 2 π n | n ∈ Z } ≈ { 6.2831853 n | n ∈ Z } x = { π ( 1 + 2 n ) | n ∈ Z } ≈ { 6.2831853 n + 3.1415927 | n ∈ Z } x = { π ( 3 + 8 n ) 4 | n ∈ Z } ≈ { 6.2831853 n + 2.3561945 | n ∈ Z } x = { π ( 7 + 8 n ) 4 | n ∈ Z } ≈ { 6.2831853 n + 5.4977871 | n ∈ Z } \begin{aligned}x &= \left\{2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(1 + 2 n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1415927\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(3 + 8 n\right)}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.3561945\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(7 + 8 n\right)}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.4977871\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned} x x x x = { 2 πn ∣ n ∈ Z } ≈ { 6.2831853 n ∣ n ∈ Z } = { π ( 1 + 2 n ) ∣ n ∈ Z } ≈ { 6.2831853 n + 3.1415927 ∣ n ∈ Z } = { 4 π ( 3 + 8 n ) n ∈ Z } ≈ { 6.2831853 n + 2.3561945 ∣ n ∈ Z } = { 4 π ( 7 + 8 n ) n ∈ Z } ≈ { 6.2831853 n + 5.4977871 ∣ n ∈ Z }
