What is the general solution for cos(x)+sin(x)tan(x)=2 ?

The general solution for cos(x)+sin(x)tan(x)=2 is x= pi/3+2pin,x=(5pi)/3+2pin

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cos(x)+sin(x)tan(x)=2

cos (x) + sin (x) tan (x) = 2

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

cos (x) + sin (x) tan (x) = 2

Subtract

2

from both sides

cos (x) + sin (x) tan (x) - 2 = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

- 2 cos (x) + 1 = 0

Move

1

to the right side

- 2 cos (x) = - 1

Divide both sides by

- 2

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

General solutions for

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (θ) = \frac{3}{3}

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

sin (10 5^{\circ})

3 tan^{3} (θ) = tan (θ)

csc^{2} (x) - 4 = 0

What is the general solution for cos(x)+sin(x)tan(x)=2 ?
The general solution for cos(x)+sin(x)tan(x)=2 is x= pi/3+2pin,x=(5pi)/3+2pin