What is the general solution for tan(x+7)=cot(4x+8) ?

The general solution for tan(x+7)=cot(4x+8) is x=-3+(2pin)/5+pi/(10),x=-3+(2pin)/5+(3pi)/(10)

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tan(x+7)=cot(4x+8)

tan (x + 7) = cot (4 x + 8)

x = - 3 + \frac{2 πn}{5} + \frac{π}{10}, x = - 3 + \frac{2 πn}{5} + \frac{3 π}{10}

Solution steps

tan (x + 7) = cot (4 x + 8)

Subtract

cot (4 x + 8)

from both sides

tan (x + 7) - cot (4 x + 8) = 0

Express with sin, cos

\frac{- cos ( 7 + x ) cos ( 8 + 4 x ) + sin ( 7 + x ) sin ( 8 + 4 x )}{cos ( 7 + x ) sin ( 8 + 4 x )} = 0

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

- cos (7 + x) cos (8 + 4 x) + sin (7 + x) sin (8 + 4 x) = 0

Rewrite using trig identities

- cos (7 + x + 8 + 4 x) = 0

Divide both sides by

- 1

cos (7 + x + 8 + 4 x) = 0

General solutions for

cos (7 + x + 8 + 4 x) = 0

7 + x + 8 + 4 x = \frac{π}{2} + 2 πn, 7 + x + 8 + 4 x = \frac{3 π}{2} + 2 πn

Solve

7 + x + 8 + 4 x = \frac{π}{2} + 2 πn : x = - 3 + \frac{2 πn}{5} + \frac{π}{10}

Solve

7 + x + 8 + 4 x = \frac{3 π}{2} + 2 πn : x = - 3 + \frac{2 πn}{5} + \frac{3 π}{10}

x = - 3 + \frac{2 πn}{5} + \frac{π}{10}, x = - 3 + \frac{2 πn}{5} + \frac{3 π}{10}

43 cos (t) - 4 sin (t) = 0

csc (θ) = - \frac{5}{2}

\frac{3}{3} = tan (θ)

x, tan (x) + 3 = 0

cos (x) = \frac{4.1}{7.9}

What is the general solution for tan(x+7)=cot(4x+8) ?
The general solution for tan(x+7)=cot(4x+8) is x=-3+(2pin)/5+pi/(10),x=-3+(2pin)/5+(3pi)/(10)