What is the general solution for tan(x)tan(7x)=1,x ?

The general solution for tan(x)tan(7x)=1,x is No Solution for x\in\mathbb{R}

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tan(x)tan(7x)=1,x

tan (x) tan (7 x) = 1, x

No Solution for x \in R

Solution steps

tan (x) tan (7 x) = 1, x

Subtract

1

from both sides

tan (x) tan (7 x) - 1 = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

- cos (7 x + x) = 0

Divide both sides by

- 1

cos (7 x + x) = 0

General solutions for

cos (7 x + x) = 0

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

Solve

7 x + x = \frac{π}{2} + 2 πn : x = \frac{π}{16} + \frac{πn}{4}

Solve

7 x + x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}, x = \frac{3 π}{16} + \frac{πn}{4}

Solutions for the range

x

No Solution for x \in R

3 sec^{2} (x) + tan (x) - 6 = 0

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

8 cos^{2} (x) + 2 cos (x) - 3 = 0

cos (A) = \frac{1}{65}, cos (B) = \frac{1}{5}

sin (θ) = 0.9063

What is the general solution for tan(x)tan(7x)=1,x ?
The general solution for tan(x)tan(7x)=1,x is No Solution for x\in\mathbb{R}