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Popular >

tan(θ)+1=sqrt(3)+sqrt(3)cot(θ)

Solution

tan (θ) + 1 = 3 + 3 cot (θ)

Solution

θ = \frac{3 π}{4} + πn, θ = \frac{π}{3} + πn

+1

Solution steps

tan (θ) + 1 = 3 + 3 cot (θ)

Subtract

3 + 3 cot (θ)

from both sides

tan (θ) + 1 - 3 - 3 cot (θ) = 0

Rewrite using trig identities

1 + \frac{1}{cot ( θ )} - 3 - cot (θ) 3 = 0

Solve by substitution

cot (θ) = - 1, cot (θ) = \frac{3}{3}

cot (θ) = - 1 : θ = \frac{3 π}{4} + πn

cot (θ) = \frac{3}{3} : θ = \frac{π}{3} + πn

Combine all the solutions

θ = \frac{3 π}{4} + πn, θ = \frac{π}{3} + πn

Popular Examples

2-2cos^2(x)=2cos^2(x/2)

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

3=4sin(8(-pi/2-x))+3

3 = 4 sin (8 (- \frac{π}{2} - x)) + 3

5 sin (x) - 7 = 0

tan(θ/2+pi/4)=-1,0<= θ<= 2pi

tan (\frac{θ}{2} + \frac{π}{4}) = - 1, 0 \leq θ \leq 2 π

sin^2(x)=2cos(x)+2,0<= x<= 2pi

sin^{2} (x) = 2 cos (x) + 2, 0 \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for tan(θ)+1=sqrt(3)+sqrt(3)cot(θ) ?
The general solution for tan(θ)+1=sqrt(3)+sqrt(3)cot(θ) is θ=(3pi)/4+pin,θ= pi/3+pin