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

The general solution for sin(x)+cos(x)*cot(x)=2 is x= pi/6+2pin,x=(5pi)/6+2pin

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sin(x)+cos(x)*cot(x)=2

sin (x) + cos (x) \cdot cot (x) = 2

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Subtract

2

from both sides

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

Express with sin, cos

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

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

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

Rewrite using trig identities

- 2 sin (x) + 1 = 0

Move

1

to the right side

- 2 sin (x) = - 1

Divide both sides by

- 2

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

General solutions for

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

4 sin (θ) = 3 sec (θ)

x, (d^{2} - 3 d + 2) y = cos (e^{- x})

tan (θ) = \frac{6}{12}

(tan (x) + 1)^{2} + (1 + \frac{1}{tan ( x )})^{2} = 100

8 cos (x + 1 0^{\circ}) = 5

What is the general solution for sin(x)+cos(x)*cot(x)=2 ?
The general solution for sin(x)+cos(x)*cot(x)=2 is x= pi/6+2pin,x=(5pi)/6+2pin