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

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

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cos(x)-tan(x)=0

cos (x) - tan (x) = 0

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

Solution steps

cos (x) - tan (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{5 - 1}{2}

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

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

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

2 sin (x) - cos (x) = 0.2

tan^{2} (x) - tan (x) = 0, 0 \leq x \leq 2 π

cos (2 x) = \frac{1}{9}

\frac{( 1 )}{( cot ( θ ) )} = \frac{- ( 7 )}{( 25 )}

tan (θ) = \frac{- 1}{- 2}

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