What is the general solution for tan(x)-cos(x)=0 ?

The general solution for tan(x)-cos(x)=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin

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tan(x)-cos(x)=0

tan (x) - cos (x) = 0

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Solution steps

tan (x) - cos (x) = 0

Express with sin, cos

\frac{- cos ^{2} ( x ) + sin ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos^{2} (x) + sin (x) = 0

Rewrite using trig identities

- 1 + sin (x) + sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{- 1 + 5}{2}, sin (x) = \frac{- 1 - 5}{2}

sin (x) = \frac{- 1 + 5}{2} : x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{- 1 - 5}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

- 8 \cdot sin (0.784 + x) = 0

6 sin^{2} (x) + 5 sin (x) + 1 = 0

3 tan^{2} (x) + 3 tan (x) = 0

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

3 tan^{2} (x) + tan (x) = 0

What is the general solution for tan(x)-cos(x)=0 ?
The general solution for tan(x)-cos(x)=0 is x=0.66623…+2pin,x=pi-0.66623…+2pin