What is the general solution for tan(x)sec(x)=tan(x) ?

The general solution for tan(x)sec(x)=tan(x) is x=pin

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tan(x)sec(x)=tan(x)

tan (x) sec (x) = tan (x)

x = πn

Solution steps

tan (x) sec (x) = tan (x)

Subtract

tan (x)

from both sides

tan (x) sec (x) - tan (x) = 0

Factor

tan (x) sec (x) - tan (x) : tan (x) (sec (x) - 1)

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

Solving each part separately

tan (x) = 0 or sec (x) - 1 = 0

tan (x) = 0 : x = πn

sec (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = πn, x = 2 πn

Merge Overlapping Intervals

x = πn

1 - sin (2 x) = cos (2 x)

sin (2 x - 5 \frac{π}{6}) = - \frac{1}{2}, 0 \leq x \leq 2 π

sin (x) = 1, 0 \leq x \leq 2 π

6 csc (θ) - 6 = 0

9 sin (x) tan (x) + 4 tan (x) = 0

What is the general solution for tan(x)sec(x)=tan(x) ?
The general solution for tan(x)sec(x)=tan(x) is x=pin